These are the current methods I am using to do Crossing Posting.

• From Mastodon to Bluesky: https://skymoth.app/.

Log in both accounts and you're ready to post toots.

• From Mastodon to X (Formerly Twitter): yinan-c/Mastodon-to-Twitter-Sync

You'll need to configure both Twitter and Mastodon API for this.

Unfortunately I did not find a good way to sync old Tweets to mastodon account in mastodon.social. Let me know if you do find something for this.