List Google calendars and choose the one to push to (Feature 16)

GET /api/v1/integrations/google/calendars trades the stored refresh token
for an access token, reads every calendarList page and answers
[{id, summary, primary, accessRole}] for writer and owner calendars only.
PUT /api/v1/integrations/google/calendar {calendar_id} validates the id
against that same filtered listing and stores calendar_id and
calendar_name; any other id is 422 unknown_calendar.

Both hold the service's account lock, answer 409 not_connected with
nothing connected, and 502 reconnect_required when Google no longer
accepts the grant, leaving the connection as it is. The gcaltest fake
gains the refresh grant and a pausable calendarList endpoint.

Maestro task 0fe3f1f2-4932-4d10-81dd-74c4f630d215.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

internal/db/querier.go

@@ -194,6 +194,8 @@ type Querier interface {
 	RedraftWeekPlan(ctx context.Context, arg RedraftWeekPlanParams) error
 	// An unknown id returns sql.ErrNoRows.
 	SetDinnerFavorite(ctx context.Context, arg SetDinnerFavoriteParams) (Dinner, error)
+	// Sets the chosen calendar; affects no row when nothing is connected.
+	SetIntegrationsGoogleCalendar(ctx context.Context, arg SetIntegrationsGoogleCalendarParams) (int64, error)
 	// Marks a pending batch running; a batch in any other status is left as
 	// it is (0 rows).
 	StartSuggestionBatch(ctx context.Context, arg StartSuggestionBatchParams) (int64, error)

internal/db/settings.sql.go

@@ -139,6 +139,27 @@ func (q *Queries) GetRecipeSearchSettings(ctx context.Context) (RecipeSearchSett
 	return i, err
 }
 
+const setIntegrationsGoogleCalendar = `-- name: SetIntegrationsGoogleCalendar :execrows
+UPDATE integrations_google
+SET calendar_id = ?, calendar_name = ?, updated_at = ?
+WHERE id = 1
+`
+
+type SetIntegrationsGoogleCalendarParams struct {
+	CalendarID   sql.NullString
+	CalendarName sql.NullString
+	UpdatedAt    string
+}
+
+// Sets the chosen calendar; affects no row when nothing is connected.
+func (q *Queries) SetIntegrationsGoogleCalendar(ctx context.Context, arg SetIntegrationsGoogleCalendarParams) (int64, error) {
+	result, err := q.db.ExecContext(ctx, setIntegrationsGoogleCalendar, arg.CalendarID, arg.CalendarName, arg.UpdatedAt)
+	if err != nil {
+		return 0, err
+	}
+	return result.RowsAffected()
+}
+
 const upsertAISettings = `-- name: UpsertAISettings :one
 INSERT INTO ai_settings (
 	id, provider, base_url, model, temperature, system_prompt, api_key_ct,