You could try copying the following files from your old profile folder -- inside the Old Firefox Data folder on your desktop -- to your currently live profile folder. Of course, Firefox should be closed when replacing its settings files.

search.json.mozlz4

The easiest way to open your current profile folder is via the Troubleshooting Information page. Either:

• "3-bar" menu button > "?" Help > Troubleshooting Information
• (menu bar) Help > Troubleshooting Information
• type or paste about:support in the address bar and press Enter

In the first table on the page, on the Profile Folder row, click the "Open Folder" button. This should launch a new window listing various files and folders in Windows Explorer.

Note: This file is mentioned in the general article: Recover important data from an old profile.

Note: If you want to pre-check the contents of a search.json.mozlz4 page, I have a decompressor here:

https://www.jeffersonscher.com/ffu/searchjson.html

unfortunately, that didn't seem to help. Instead it reset my default search engine back to Google and presumably would've reset any additional engines if I had added any to this profile. Fortunately, restoring the file that was originally in the new profile (I renamed it instead of overwriting it with the file from the "old" profile) saved me the few clicks of navigating to my search settings, but the problem remains that I may have to "manually" add all of my favorite engines back. Is there anything else I could try (another file perhaps), or is that pretty much is it?

I'll also take a look at that "recovering important data from an old profile" article in case that helps with this or anything else I might be missing without realizing it. Thanks for linking it!

Are you sure the missing search engines are in the old file you tried using?

if that's the file that supposed to contain search engine preferences, I'm almost positive, but if I think of it next time I'm on that computer, I'll try copying the same file from this laptop's Firefox profile, because I know this profile has a bunch of search engines installed. In the meantime, do you know anything else that might explain my predicament?

I can't think of anything else. Either the file has the data or it doesn't...

weird. In any case, I've slowly but surely been rebuilding the search engine preferences, so at least I'm making progress working around my issue? I'll let you know if the file from this computer's profile works, but beyond that, I guess there's no use continuing the conversation. Thanks so much for trying; I don't think I would've even gotten as far as switching switching a relevant file on my own.