It's not yesterday, it was 20 years ago when Google excelled at exact keyword matches. It has been a constant evolution away from that.

I hate the new Google as much as others, but if you don't adapt your search habits for 20 years when the whole ecosystem around you has been obviously changing, that's kind of on you. Just use another search engine that fits your use case. Personally I use Kagi and I haven't touched Google for the last year at all.

Does Kagi support queries like site, inurl, intitle, etc or have some similar capabilities?

Yes.

Yep, it's time to give up on Google... Both the search engine and the company. Kagi Fastmail Rsync.net

These are worth paying for.

seconding fastmail - i was grandfathered at $5 a year for years, i pay $15 now i think - and i am probably going to pay for kagi (or ilk). I run nextcloud, after trying other things like syncthing and owncloud - as well as owning a synology i would never put on the public internet.