If you use Sync then best is to disconnect Sync temporarily during troubleshooting.

You can check for issues with the places.sqlite and favicons.sqlite databases in the Firefox profile folder.

• use the "Places Database" -> "Verify Integrity" button on the "Help -> More Troubleshooting Information" (about:support) page

If errors are reported with "Verify Integrity", close and restart Firefox or reboot and retry.

If "Verify Integrity" cannot repair places.sqlite, rename/remove all places.sqlite and favicons.sqlite files in the Firefox profile folder with Firefox closed. Firefox will rebuild places.sqlite and restore the bookmarks from the most recent JSON backup in the bookmarkbackups folder.

• keep a backup copy of places.sqlite in case a new places.sqlite database has to be created
• you lose the history when a new places.sqlite is created

You may have to restore an older bookmarks backup in the bookmarkbackups folder via the Bookmarks Manager (Library).

• Bookmarks -> Show All Bookmarks -> Import & Backup -> Restore
• https://support.mozilla.org/en-US/kb/restore-bookmarks-from-backup-or-move-them

See also:

• https://support.mozilla.org/en-US/kb/Bookmarks+not+saved#w_fix-the-bookmarks-file
• https://support.mozilla.org/en-US/kb/fix-bookmarks-and-history-will-not-be-functional

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 about:profiles page.

• Help -> More Troubleshooting Information -> Profile Folder/Directory:
  Windows: Open Folder; Linux: Open Directory; Mac: Show in Finder
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

Look like I have to remove the files in question, reboot or restart did not repair the error. > Task: checkIntegrity - Unable to check places.sqlite integrity: Error: Error(s) encountered during statement execution: database disk image is malformed > Task: invalidateCaches - The task queue was cleared by an error in another task. > Task: checkCoherence - The task queue was cleared by an error in another task. > Task: expire - The task queue was cleared by an error in another task. > Task: originFrecencyStats - The task queue was cleared by an error in another task. > Task: vacuum - The task queue was cleared by an error in another task. > Task: stats - The task queue was cleared by an error in another task. > Task: _refreshUI - The task queue was cleared by an error in another task.

Moved all the places.sqlite and favicons.sqlite to trash, restart Firefox, check integrity, still look the same: > Task: checkIntegrity - Unable to check places.sqlite integrity: Error: Error(s) encountered during statement execution: database disk image is malformed > Task: invalidateCaches - The task queue was cleared by an error in another task. > Task: checkCoherence - The task queue was cleared by an error in another task. > Task: expire - The task queue was cleared by an error in another task. > Task: originFrecencyStats - The task queue was cleared by an error in another task. > Task: vacuum - The task queue was cleared by an error in another task. > Task: stats - The task queue was cleared by an error in another task. > Task: _refreshUI - The task queue was cleared by an error in another task.

places.sqlite and favicons.sqlite are no longer exist. Firefox does not recreate them. Perhaps Firefox never access those files before I move them to trash.

If Firefox doesn't create new files then thus likely means that you didn't remove these files in the correct location.

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 about:profiles page.

• Help -> More Troubleshooting Information -> Profile Folder/Directory:
  Windows: Open Folder; Linux: Open Directory; Mac: Show in Finder
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

Finder found many files with the same (or similar) name to places.sqlite and favicons.sqlite. I did not check where the files are. The date last opened are all --, so I thought these file were never accessed. I moved them all to trash. I take a look in the trash folder and highlighted them (see attached screenshot). Some of them now have the move to trash time appended at the end, once, twice or thrice (I guess). I put them back I found them in several folders: ifbh0447.default-1615345693863, aesc86xg.default-159878051638, 9gh3e57s-1.default-1550734256672, etc.. all has been rename (time stamps appended) by moving to trash and back. There are 6 files without time stamp stay put in the trash and would not budge or do not have the option to be put back. The nearest recent date modified (of the files in question) is Mar 30, 2021, before I migrate to the new Mac mini with the M1 chip. I suspect my new Mac is so fast, Firefox never had a chance to modify these files before the OSX cleared the task queue.