feat: show agent badge on workspace list (#23453)

- Adds `GET /api/experimental/chats/by-workspace` endpoint that returns
workspace_id → latest chat_id mapping
- Modifies FE to fetch this alongside the workspace list, gated on
`agents` experiment and render an "Agent" badge similar to the existing
"Task" badge in `WorkspacesTable`
- Badge links to the "latest chat" linked to the given workspace.

Notes:
- Intentionally uses `fetchWithPostFilter` for RBAC to decouple from
workspaces API — will migrate to `workspaces_expanded` view later.
- If users have multiple chats linked to the same workspace, the badge
will link to the most recently updated one.

> 🤖 This PR was created with the help of Coder Agents, and has been
reviewed by my human. 🧑‍💻

coderd/database/queries/chats.sql

@@ -889,6 +889,13 @@ JOIN group_members_expanded gme ON gme.group_id = g.id
 WHERE gme.user_id = @user_id::uuid
   AND g.chat_spend_limit_micros IS NOT NULL;
 
+-- name: GetChatsByWorkspaceIDs :many
+SELECT *
+FROM chats
+WHERE archived = false
+  AND workspace_id = ANY(@ids::uuid[])
+ORDER BY workspace_id, updated_at DESC;
+
 -- name: ResolveUserChatSpendLimit :one
 -- Resolves the effective spend limit for a user using the hierarchy:
 -- 1. Individual user override (highest priority)