feat(coderd): add task prompt modification endpoint (#20811)

This PR adds the backend implementation for modifying task prompts. Part
of https://github.com/coder/internal/issues/1084

## Changes

- New `UpdateTaskPrompt` database query to update task prompts
- New PATCH `/api/v2/tasks/{task}/prompt` endpoint

## Notes

This is part 1 of a 2-part PR stack. The frontend UI will be added in a
follow-up PR based on this branch
(https://github.com/coder/coder/pull/20812).

---

🤖 PR was written by Claude Sonnet 4.5 Thinking using [Coder
Mux](https://github.com/coder/cmux) and reviewed by a human 👩

coderd/database/queries.sql.go

@@ -13425,6 +13425,40 @@ func (q *sqlQuerier) ListTasks(ctx context.Context, arg ListTasksParams) ([]Task
 	return items, nil
 }
 
+const updateTaskPrompt = `-- name: UpdateTaskPrompt :one
+UPDATE
+	tasks
+SET
+	prompt = $1::text
+WHERE
+	id = $2::uuid
+	AND deleted_at IS NULL
+RETURNING id, organization_id, owner_id, name, workspace_id, template_version_id, template_parameters, prompt, created_at, deleted_at
+`
+
+type UpdateTaskPromptParams struct {
+	Prompt string    `db:"prompt" json:"prompt"`
+	ID     uuid.UUID `db:"id" json:"id"`
+}
+
+func (q *sqlQuerier) UpdateTaskPrompt(ctx context.Context, arg UpdateTaskPromptParams) (TaskTable, error) {
+	row := q.db.QueryRowContext(ctx, updateTaskPrompt, arg.Prompt, arg.ID)
+	var i TaskTable
+	err := row.Scan(
+		&i.ID,
+		&i.OrganizationID,
+		&i.OwnerID,
+		&i.Name,
+		&i.WorkspaceID,
+		&i.TemplateVersionID,
+		&i.TemplateParameters,
+		&i.Prompt,
+		&i.CreatedAt,
+		&i.DeletedAt,
+	)
+	return i, err
+}
+
 const updateTaskWorkspaceID = `-- name: UpdateTaskWorkspaceID :one
 UPDATE
 	tasks