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/aitasks_test.go

@@ -1049,14 +1049,17 @@ func TestTasksCreate(t *testing.T) {
 		t.Parallel()
 
 		tests := []struct {
-			name               string
-			taskName           string
-			expectFallbackName bool
-			expectError        string
+			name                      string
+			taskName                  string
+			taskDisplayName           string
+			expectFallbackName        bool
+			expectFallbackDisplayName bool
+			expectError               string
 		}{
 			{
-				name:     "ValidName",
-				taskName: "a-valid-task-name",
+				name:                      "ValidName",
+				taskName:                  "a-valid-task-name",
+				expectFallbackDisplayName: true,
 			},
 			{
 				name:        "NotValidName",
@@ -1066,8 +1069,37 @@ func TestTasksCreate(t *testing.T) {
 			{
 				name:               "NoNameProvided",
 				taskName:           "",
+				taskDisplayName:    "A valid task display name",
 				expectFallbackName: true,
 			},
+			{
+				name:               "ValidDisplayName",
+				taskDisplayName:    "A valid task display name",
+				expectFallbackName: true,
+			},
+			{
+				name:            "NotValidDisplayName",
+				taskDisplayName: "This is a task display name with a length greater than 64 characters.",
+				expectError:     "Display name must be 64 characters or less.",
+			},
+			{
+				name:                      "NoDisplayNameProvided",
+				taskName:                  "a-valid-task-name",
+				taskDisplayName:           "",
+				expectFallbackDisplayName: true,
+			},
+			{
+				name:            "ValidNameAndDisplayName",
+				taskName:        "a-valid-task-name",
+				taskDisplayName: "A valid task display name",
+			},
+			{
+				name:                      "NoNameAndDisplayNameProvided",
+				taskName:                  "",
+				taskDisplayName:           "",
+				expectFallbackName:        true,
+				expectFallbackDisplayName: true,
+			},
 		}
 
 		for _, tt := range tests {
@@ -1098,6 +1130,7 @@ func TestTasksCreate(t *testing.T) {
 					TemplateVersionID: template.ActiveVersionID,
 					Input:             "Some prompt",
 					Name:              tt.taskName,
+					DisplayName:       tt.taskDisplayName,
 				})
 				if tt.expectError == "" {
 					require.NoError(t, err)
@@ -1111,8 +1144,17 @@ func TestTasksCreate(t *testing.T) {
 					if !tt.expectFallbackName {
 						require.Equal(t, tt.taskName, task.Name)
 					}
+
+					// Then: We expect the correct display name to have been picked.
+					require.NotEmpty(t, task.DisplayName)
+					if !tt.expectFallbackDisplayName {
+						require.Equal(t, tt.taskDisplayName, task.DisplayName)
+					}
 				} else {
-					require.ErrorContains(t, err, tt.expectError)
+					var apiErr *codersdk.Error
+					require.ErrorAs(t, err, &apiErr)
+					require.Equal(t, http.StatusBadRequest, apiErr.StatusCode())
+					require.Equal(t, apiErr.Message, tt.expectError)
 				}
 			})
 		}