See if you can get the old hard drive and mount it to your new system as an external drive.

Thanks. The Amac center did copy all the data from the hard drive of the old Mac to the new Mac; but they say that bookmarks were not on the hard drive, so they can not be copied.

There are some backup files on the MacBook and on the external drive, with bookmarks such as

bookmarks-2021-09-25_4902_sHoE2MCssyntcCX9EOI0OQ==.jsonlz4

Can those be copied to Firefox and/or Safari?

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

• ~/Library/Application Support/Firefox/Profiles/<profile>

In Mac OS X v10.7 and later, the "~/Library" folder in the Home directory is a hidden folder.

• https://www.macworld.co.uk/how-to/mac-software/hidden-files-mac-3520878/

The places.sqlite file contains your History and Bookmarks.

. . . . with bookmarks such as bookmarks-2021-09-25_4902_sHoE2MCssyntcCX9EOI0OQ==.jsonlz4

That is a backup file. Only Firefox can open it.

Restore Bookmark Backups

Firefox automatically makes backups of the bookmarks. These are stored in the bookmarkbackups folder.

Open the Bookmarks Manager; Press the Alt or F10 key to bring up the toolbar, and select Bookmarks. Hot key is <Control> (Mac=<Command>) <Shift> B. Firefox 84+ <Control> (Mac=<Command>) <Shift> O.

Once the window is open, at the top of the page, press the button labeled Import and Backup. Select Restore. From the list, pick the file you want and click it.

The backups are stored in a jsonlz4 file named something like this; bookmarks-2016-06-29_1424_enD1GTH ya0JmicnYWg4V4g==.jsonlz4

In this example; 2016-06-29 = date created, 1424 = number of entries.

https://support.mozilla.org/en-US/kb/restore-bookmarks-from-backup-or-move-them

https://support.mozilla.org/en-US/kb/recover-lost-or-missing-bookmarks

https://support.mozilla.org/kb/forum-response-recover-bookmarks-after-update

http://kb.mozillazine.org/Unable_to_process_the_backup_file_-_Firefox

jscher2000 has a tool on his website to extract out your bookmarks and save them to an HTML-format bookmark export file. If you want to try it, here is the page:

https://www.jeffersonscher.com/res/bookbackreader.html

To open the bookmarkbackups folder in Finder, use the "Open in Finder" button in the first table on the Troubleshooting Information page, and double-click into bookmarkbackups where you should see several dated files. From there you can drag and drop onto the conversion tool.

To import the HTML file, see the steps in this article: Import Bookmarks from an HTML file.