Are you using the built-in Google search engine? When I do an address bar search for tomatoes, I get this results page:

https://www.google.com/search?client=firefox-b-1-d&q=tomatoes

Does your results page URL look like that or does it have different parameters?

One thing I noticed about "People also ask" is that it those sections now contain an AI Summary, which slows them down a bit.

No, when I do search, I get a lot of gibberish after =tomatoes. URL never looks clean like yours.

BTW, I opened page with "tomato", then restarted FF in troubleshoot mode. Old tomato page doesn't open "people search also" tabs, while new search page with "tomato" opened already in troubleshoot mode, opens them without problem, I can click them.

Once you start interacting with Google results pages, it does add a lot of stuff to the URL, but when you just submit a word in the address bar, do you get the clean-looking URL?

If you get a different URL from an address bar search, this could be caused by changing the default search engine through an add-on or through a custom URL. Some users do this to remove the AI summary section, but in other cases, it might not be intentional/desirable. If you check the search engine settings, can you change back to the built-in Google search engine? See: Manage Firefox search settings.

Reading back to your original question, you said that Google also does not work normally in a new profile -- presumably that was without syncing over settings from your regular profile. Do you use any external security software that might modify URLs sent to Google?