I understand that there was pinned content on the previous version of Firefox in the tiles page. Unfortunately this is not a feature that is saved.

However the url for the source download is located in this about:config entry:

browser.newtabpage.directory.ping

with the url https://tiles.services.mozilla.com/v3/links/ it will give you a json file.

I'm not sure what kind of pins you are referring to -- pinned sites on the "new tab" page, pinned tabs (part of your session history), or another kind of pin, perhaps something added by an add-on? Could you clarify that?

Also, one possible reason for losing data after an update is if the Firefox Refresh feature ran. This could occur when Firefox says it is starting slowly and you can speed it up by restoring some default settings. If you click that button, your old settings folder is moved to the desktop inside an Old Firefox Data folder. Do you see anything like that? If so, hold onto it and we might be able to help you dig out what you're looking for.