Sync is your friend, but it's not a back up service. see screenshot https://support.mozilla.org/en-US/kb/how-do-i-set-sync-my-computer# https://support.mozilla.org/en-US/kb/how-do-i-choose-what-information-sync-firefox#

Once both computers have the same Mozilla account, then from win11 you can see the open tabs on the win10 and open them.

Firefox uses two locations in the hidden "AppData" location for the Firefox profile folder. One location in "AppData\Roaming" for personal data like bookmarks and logins and another location in "AppData\Local" for temporary files like the disk cache, so make sure to look in the correct location.

Primary location used for the main profile that keeps your personal data (Root Directory on about:profiles).

• C:\Users\<user>\AppData\Roaming\Mozilla\Firefox\Profiles\<profile>

You can copy certain files with Firefox closed from one profile folder to another profile folder to transfer personal data. Note that best is to avoid restoring a full profile folder and only restore important files that are safe to restore/transfer.

• bookmarks and history: places.sqlite
• favicons: favicons.sqlite
• bookmark backups: compressed .jsonlz4 JSON backups in the bookmarkbackups folder
• cookies.sqlite for the Cookies
• formhistory.sqlite for saved autocomplete Form Data
• logins.json (encrypted logins) and key4.db (encryption key/primary password) for logins saved in the Password Manager
• cert9.db for certificates stored in the Certificate Manager
• persdict.dat for words added to the spell checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other website specific data (Site Preferences)
• sessionstore.jsonlz4 for open tabs and pinned tabs (see also the sessionstore-backups folder)

Hello

Other illustration https://connect.mozilla.org/t5/discussions/upgrading-your-computer-and-moving-your-firefox-data/m-p/48032/highlight/true#M17142 for my part