feat: add display name field for tasks (#20856)

## Problem

Tasks currently only expose a machine-friendly name field (e.g.
`task-python-debug-a1b2`), but this value is primarily an identifier
rather than a clean, descriptive label. We need a separate
display-friendly name for use in the UI.

This PR introduces a new `display_name` field and updates the task-name
generation flow. The Claude system prompt was updated to return valid
JSON with both `name` and `display_name`. The name generation logic
follows a fallback chain (Anthropic > prompt sanitization > random
fallback). To make task names more closely resemble their display names,
the legacy `task-` prefix has been removed. For context, PR
https://github.com/coder/coder/pull/20834 introduced a small Task icon
to the workspace list to help identify workspaces associated to tasks.

## Changes

- Database migration: Added `display_name` column to tasks table
- Updated system prompt to generate both task name and display name as
valid JSON
- Task name generation now follows a fallback chain: Anthropic > prompt
sanitization > random fallback
- Removed `task-` prefix from task names to allow more descriptive names
- Note: PR https://github.com/coder/coder/pull/20834 adds a Task icon to
workspaces in the workspace list to distinguish task-created workspaces

**Note:** UI changes will be addressed in a follow-up PR

Related to: https://github.com/coder/coder/issues/20801

coderd/database/migrations/000400_add_task_display_name.down.sql

@@ -0,0 +1,87 @@
+-- Drop view first before removing the display_name column from tasks
+DROP VIEW IF EXISTS tasks_with_status;
+
+-- Remove display_name column from tasks
+ALTER TABLE tasks DROP COLUMN display_name;
+
+-- Recreate view without the display_name column.
+-- This restores the view to its previous state after removing display_name from tasks.
+CREATE VIEW
+	tasks_with_status
+AS
+SELECT
+	tasks.*,
+	CASE
+		WHEN tasks.workspace_id IS NULL OR latest_build.job_status IS NULL THEN 'pending'::task_status
+
+		WHEN latest_build.job_status = 'failed' THEN 'error'::task_status
+
+		WHEN latest_build.transition IN ('stop', 'delete')
+			AND latest_build.job_status = 'succeeded' THEN 'paused'::task_status
+
+		WHEN latest_build.transition = 'start'
+			AND latest_build.job_status = 'pending' THEN 'initializing'::task_status
+
+		WHEN latest_build.transition = 'start' AND latest_build.job_status IN ('running', 'succeeded') THEN
+			CASE
+				WHEN agent_status.none THEN 'initializing'::task_status
+				WHEN agent_status.connecting THEN 'initializing'::task_status
+				WHEN agent_status.connected THEN
+					CASE
+						WHEN app_status.any_unhealthy THEN 'error'::task_status
+						WHEN app_status.any_initializing THEN 'initializing'::task_status
+						WHEN app_status.all_healthy_or_disabled THEN 'active'::task_status
+						ELSE 'unknown'::task_status
+						END
+				ELSE 'unknown'::task_status
+				END
+
+		ELSE 'unknown'::task_status
+		END AS status,
+	task_app.*,
+	task_owner.*
+FROM
+	tasks
+		CROSS JOIN LATERAL (
+		SELECT
+			vu.username AS owner_username,
+			vu.name AS owner_name,
+			vu.avatar_url AS owner_avatar_url
+		FROM visible_users vu
+		WHERE vu.id = tasks.owner_id
+			) task_owner
+		LEFT JOIN LATERAL (
+		SELECT workspace_build_number, workspace_agent_id, workspace_app_id
+		FROM task_workspace_apps task_app
+		WHERE task_id = tasks.id
+		ORDER BY workspace_build_number DESC
+			LIMIT 1
+	) task_app ON TRUE
+	LEFT JOIN LATERAL (
+		SELECT
+			workspace_build.transition,
+			provisioner_job.job_status,
+			workspace_build.job_id
+		FROM workspace_builds workspace_build
+		JOIN provisioner_jobs provisioner_job ON provisioner_job.id = workspace_build.job_id
+		WHERE workspace_build.workspace_id = tasks.workspace_id
+			AND workspace_build.build_number = task_app.workspace_build_number
+	) latest_build ON TRUE
+	CROSS JOIN LATERAL (
+		SELECT
+			COUNT(*) = 0 AS none,
+			bool_or(workspace_agent.lifecycle_state IN ('created', 'starting')) AS connecting,
+			bool_and(workspace_agent.lifecycle_state = 'ready') AS connected
+		FROM workspace_agents workspace_agent
+		WHERE workspace_agent.id = task_app.workspace_agent_id
+	) agent_status
+	CROSS JOIN LATERAL (
+		SELECT
+			bool_or(workspace_app.health = 'unhealthy') AS any_unhealthy,
+			bool_or(workspace_app.health = 'initializing') AS any_initializing,
+			bool_and(workspace_app.health IN ('healthy', 'disabled')) AS all_healthy_or_disabled
+		FROM workspace_apps workspace_app
+		WHERE workspace_app.id = task_app.workspace_app_id
+	) app_status
+	WHERE
+		tasks.deleted_at IS NULL;

coderd/database/migrations/000400_add_task_display_name.up.sql

@@ -0,0 +1,158 @@
+-- Add display_name column to tasks table
+ALTER TABLE tasks ADD COLUMN display_name VARCHAR(127) NOT NULL DEFAULT '';
+COMMENT ON COLUMN tasks.display_name IS 'Display name is a custom, human-friendly task name.';
+
+-- Backfill existing tasks with truncated prompt as display name
+-- Replace newlines/tabs with spaces, truncate to 64 characters and add ellipsis if truncated
+UPDATE tasks
+SET display_name = CASE
+	WHEN LENGTH(REGEXP_REPLACE(prompt, E'[\\n\\r\\t]+', ' ', 'g')) > 64
+	THEN LEFT(REGEXP_REPLACE(prompt, E'[\\n\\r\\t]+', ' ', 'g'), 63) || '…'
+	ELSE REGEXP_REPLACE(prompt, E'[\\n\\r\\t]+', ' ', 'g')
+	END
+WHERE display_name = '';
+
+-- Recreate the tasks_with_status view to pick up the new display_name column.
+-- PostgreSQL resolves the tasks.* wildcard when the view is created, not when
+-- it's queried, so the view must be recreated after adding columns to tasks.
+DROP VIEW IF EXISTS tasks_with_status;
+
+CREATE VIEW
+	tasks_with_status
+AS
+SELECT
+	tasks.*,
+	-- Combine component statuses with precedence: build -> agent -> app.
+	CASE
+		WHEN tasks.workspace_id IS NULL THEN 'pending'::task_status
+		WHEN build_status.status != 'active' THEN build_status.status::task_status
+		WHEN agent_status.status != 'active' THEN agent_status.status::task_status
+		ELSE app_status.status::task_status
+		END AS status,
+	-- Attach debug information for troubleshooting status.
+	jsonb_build_object(
+		'build', jsonb_build_object(
+		'transition', latest_build_raw.transition,
+		'job_status', latest_build_raw.job_status,
+		'computed', build_status.status
+				 ),
+		'agent', jsonb_build_object(
+			'lifecycle_state', agent_raw.lifecycle_state,
+			'computed', agent_status.status
+				 ),
+		'app', jsonb_build_object(
+			'health', app_raw.health,
+			'computed', app_status.status
+			   )
+	) AS status_debug,
+	task_app.*,
+	agent_raw.lifecycle_state AS workspace_agent_lifecycle_state,
+	app_raw.health AS workspace_app_health,
+	task_owner.*
+FROM
+	tasks
+		CROSS JOIN LATERAL (
+		SELECT
+			vu.username AS owner_username,
+			vu.name AS owner_name,
+			vu.avatar_url AS owner_avatar_url
+		FROM
+			visible_users vu
+		WHERE
+			vu.id = tasks.owner_id
+			) task_owner
+		LEFT JOIN LATERAL (
+		SELECT
+			task_app.workspace_build_number,
+			task_app.workspace_agent_id,
+			task_app.workspace_app_id
+		FROM
+			task_workspace_apps task_app
+		WHERE
+			task_id = tasks.id
+		ORDER BY
+			task_app.workspace_build_number DESC
+			LIMIT 1
+	) task_app ON TRUE
+
+	-- Join the raw data for computing task status.
+	LEFT JOIN LATERAL (
+		SELECT
+			workspace_build.transition,
+			provisioner_job.job_status,
+			workspace_build.job_id
+		FROM
+			workspace_builds workspace_build
+		JOIN
+			provisioner_jobs provisioner_job
+			ON provisioner_job.id = workspace_build.job_id
+		WHERE
+			workspace_build.workspace_id = tasks.workspace_id
+			AND workspace_build.build_number = task_app.workspace_build_number
+	) latest_build_raw ON TRUE
+	LEFT JOIN LATERAL (
+		SELECT
+			workspace_agent.lifecycle_state
+		FROM
+			workspace_agents workspace_agent
+		WHERE
+			workspace_agent.id = task_app.workspace_agent_id
+	) agent_raw ON TRUE
+	LEFT JOIN LATERAL (
+		SELECT
+			workspace_app.health
+		FROM
+			workspace_apps workspace_app
+		WHERE
+			workspace_app.id = task_app.workspace_app_id
+	) app_raw ON TRUE
+
+	-- Compute the status for each component.
+	CROSS JOIN LATERAL (
+		SELECT
+			CASE
+				WHEN latest_build_raw.job_status IS NULL THEN 'pending'::task_status
+				WHEN latest_build_raw.job_status IN ('failed', 'canceling', 'canceled') THEN 'error'::task_status
+				WHEN
+					latest_build_raw.transition IN ('stop', 'delete')
+					AND latest_build_raw.job_status = 'succeeded' THEN 'paused'::task_status
+				WHEN
+					latest_build_raw.transition = 'start'
+					AND latest_build_raw.job_status = 'pending' THEN 'initializing'::task_status
+				-- Build is running or done, defer to agent/app status.
+				WHEN
+					latest_build_raw.transition = 'start'
+					AND latest_build_raw.job_status IN ('running', 'succeeded') THEN 'active'::task_status
+				ELSE 'unknown'::task_status
+			END AS status
+	) build_status
+	CROSS JOIN LATERAL (
+		SELECT
+			CASE
+				-- No agent or connecting.
+				WHEN
+					agent_raw.lifecycle_state IS NULL
+					OR agent_raw.lifecycle_state IN ('created', 'starting') THEN 'initializing'::task_status
+				-- Agent is running, defer to app status.
+				-- NOTE(mafredri): The start_error/start_timeout states means connected, but some startup script failed.
+				-- This may or may not affect the task status but this has to be caught by app health check.
+				WHEN agent_raw.lifecycle_state IN ('ready', 'start_timeout', 'start_error') THEN 'active'::task_status
+				-- If the agent is shutting down or turned off, this is an unknown state because we would expect a stop
+				-- build to be running.
+				-- This is essentially equal to: `IN ('shutting_down', 'shutdown_timeout', 'shutdown_error', 'off')`,
+				-- but we cannot use them because the values were added in a migration.
+				WHEN agent_raw.lifecycle_state NOT IN ('created', 'starting', 'ready', 'start_timeout', 'start_error') THEN 'unknown'::task_status
+				ELSE 'unknown'::task_status
+			END AS status
+	) agent_status
+	CROSS JOIN LATERAL (
+		SELECT
+			CASE
+				WHEN app_raw.health = 'initializing' THEN 'initializing'::task_status
+				WHEN app_raw.health = 'unhealthy' THEN 'error'::task_status
+				WHEN app_raw.health IN ('healthy', 'disabled') THEN 'active'::task_status
+				ELSE 'unknown'::task_status
+			END AS status
+	) app_status
+	WHERE
+		tasks.deleted_at IS NULL;