replace gmail resync with Gmail REST API, remove mbsync dependency

First sync still uses IMAP with app password. Subsequent syncs use
Gmail API history.list + messages.get with OAuth for faster, more
reliable incremental sync. Dispatch gmail-sync handler for gmail
accounts instead of generic email-sync. Show sync button for synced
accounts.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/servers/data-path.ts

@@ -69,7 +69,6 @@ export const getAttachmentsDir = (email: string, sessionId: string) => join(DATA
 
 export const getUserEmailDir = (email: string) => join(DATA_PATH, email, 'Gmail', 'emails');
 
-export const getMaildirPath = (email: string) => join(DATA_PATH, email, 'Gmail', 'Maildir');
 
 /** Derive a valid Linux username from a display username or email. */
 export const toShellUsername = (username: string, email: string): string => {