feat(coderd): add pagination to chat list endpoint (#22887)

Adds offset and cursor-based pagination to the `GET
/api/experimental/chats` endpoint, following the exact same patterns
used by `GetUsers` and `GetTemplateVersionsByTemplateID`.

## Changes

### Database
- Add `after_id`, `offset_opt`, `limit_opt` params to
`GetChatsByOwnerID` SQL query
- Use composite `(updated_at, id) DESC` cursor for stable, deterministic
pagination
- Add migration with composite index on `chats (owner_id, updated_at
DESC, id DESC)`

### Backend
- Use `ParsePagination()` in `listChats` handler (matches `users.go`
pattern)
- Add `Pagination` field to `ListChatsOptions` SDK struct

### Frontend
- Add `infiniteChats()` query factory using `useInfiniteQuery` with
offset-based page params (same pattern as `infiniteWorkspaceBuilds`)
- Update `AgentsPage` to use `useInfiniteQuery`
- Add "Show more" button at the bottom of the agents sidebar (matches
`HistorySidebar` pattern)
- Keep existing `chats()` query for non-paginated uses (e.g., parent
chat lookup in `AgentDetail`)

### Tests
- Add `TestListChats/Pagination` covering `limit`, `after_id` cursor,
`offset`, and no-limit behavior

coderd/database/dump.sql

@@ -3534,6 +3534,8 @@ CREATE INDEX idx_chats_last_model_config_id ON chats USING btree (last_model_con
 
 CREATE INDEX idx_chats_owner ON chats USING btree (owner_id);
 
+CREATE INDEX idx_chats_owner_updated_id ON chats USING btree (owner_id, updated_at DESC, id DESC);
+
 CREATE INDEX idx_chats_parent_chat_id ON chats USING btree (parent_chat_id);
 
 CREATE INDEX idx_chats_pending ON chats USING btree (status) WHERE (status = 'pending'::chat_status);

coderd/database/migrations/000430_chat_pagination_index.down.sql

@@ -0,0 +1 @@
+DROP INDEX IF EXISTS idx_chats_owner_updated_id;

coderd/database/migrations/000430_chat_pagination_index.up.sql

@@ -0,0 +1 @@
+CREATE INDEX idx_chats_owner_updated_id ON chats (owner_id, updated_at DESC, id DESC);

coderd/database/queries.sql.go

@@ -3454,17 +3454,51 @@ WHERE
         WHEN $2 :: boolean IS NULL THEN true
         ELSE chats.archived = $2 :: boolean
     END
+    AND CASE
+        -- This allows using the last element on a page as effectively a cursor.
+        -- This is an important option for scripts that need to paginate without
+        -- duplicating or missing data.
+        WHEN $3 :: uuid != '00000000-0000-0000-0000-000000000000'::uuid THEN (
+            -- The pagination cursor is the last ID of the previous page.
+            -- The query is ordered by the updated_at field, so select all
+            -- rows before the cursor.
+            (updated_at, id) < (
+                SELECT
+                    updated_at, id
+                FROM
+                    chats
+                WHERE
+                    id = $3
+            )
+        )
+        ELSE true
+    END
 ORDER BY
-    updated_at DESC
+    -- Deterministic and consistent ordering of all rows, even if they share
+    -- a timestamp. This is to ensure consistent pagination.
+    (updated_at, id) DESC OFFSET $4
+LIMIT
+    -- The chat list is unbounded and expected to grow large.
+    -- Default to 50 to prevent accidental excessively large queries.
+    COALESCE(NULLIF($5 :: int, 0), 50)
 `
 
 type GetChatsByOwnerIDParams struct {
-	OwnerID  uuid.UUID    `db:"owner_id" json:"owner_id"`
-	Archived sql.NullBool `db:"archived" json:"archived"`
+	OwnerID   uuid.UUID    `db:"owner_id" json:"owner_id"`
+	Archived  sql.NullBool `db:"archived" json:"archived"`
+	AfterID   uuid.UUID    `db:"after_id" json:"after_id"`
+	OffsetOpt int32        `db:"offset_opt" json:"offset_opt"`
+	LimitOpt  int32        `db:"limit_opt" json:"limit_opt"`
 }
 
 func (q *sqlQuerier) GetChatsByOwnerID(ctx context.Context, arg GetChatsByOwnerIDParams) ([]Chat, error) {
-	rows, err := q.db.QueryContext(ctx, getChatsByOwnerID, arg.OwnerID, arg.Archived)
+	rows, err := q.db.QueryContext(ctx, getChatsByOwnerID,
+		arg.OwnerID,
+		arg.Archived,
+		arg.AfterID,
+		arg.OffsetOpt,
+		arg.LimitOpt,
+	)
 	if err != nil {
 		return nil, err
 	}

coderd/database/queries/chats.sql

@@ -113,8 +113,33 @@ WHERE
         WHEN sqlc.narg('archived') :: boolean IS NULL THEN true
         ELSE chats.archived = sqlc.narg('archived') :: boolean
     END
+    AND CASE
+        -- This allows using the last element on a page as effectively a cursor.
+        -- This is an important option for scripts that need to paginate without
+        -- duplicating or missing data.
+        WHEN @after_id :: uuid != '00000000-0000-0000-0000-000000000000'::uuid THEN (
+            -- The pagination cursor is the last ID of the previous page.
+            -- The query is ordered by the updated_at field, so select all
+            -- rows before the cursor.
+            (updated_at, id) < (
+                SELECT
+                    updated_at, id
+                FROM
+                    chats
+                WHERE
+                    id = @after_id
+            )
+        )
+        ELSE true
+    END
 ORDER BY
-    updated_at DESC;
+    -- Deterministic and consistent ordering of all rows, even if they share
+    -- a timestamp. This is to ensure consistent pagination.
+    (updated_at, id) DESC OFFSET @offset_opt
+LIMIT
+    -- The chat list is unbounded and expected to grow large.
+    -- Default to 50 to prevent accidental excessively large queries.
+    COALESCE(NULLIF(@limit_opt :: int, 0), 50);
 
 -- name: ListChildChatsByParentID :many
 SELECT