Firefox account is for sync, it doesn't work well as a backup. You need a full backup.

How do I back it up? From what I can see it only backs up bookmarked history.

Please read [[Back up and restore information in Firefox profiles]].

There is no backup of the browsing history, so your only option is to backup the places.sqlite database (bookmarks and history). *https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles You can copy certain files with Firefox closed to the current profile folder to transfer or recover personal data. Note that best is to avoid copying a full profile folder. You can use the button on the "Help -> More Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the <b>about:profiles</b> page (Root directory). *Help -> More Troubleshooting Information -> Profile Folder/Directory:<br>Windows: Open Folder; Linux: Open Directory; Mac: Show in Finder *https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data <hr> *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;32+) and key4.db (decryption key;58+) for Passwords saved in the Password Manager<br>key3.db support ended in 73+; to use key3.db in 58-72, make sure to remove key4.db *cert9.db (58+) for (intermediate) 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)