I would assume they will do fingerprinting based on meta data such as op address and browser type as well. I suggest using yewtu.be or https://piped.kavin.rocks/ as alternative front end and some tracker blocking. Personally I use Nextdns for queries and on my desktop the librefox browser and protonvpn. I just got to know the Orion browser that looks interesting as well.

Google may still be able to figure out it’s you because of your cookies and anything else that is unique to you.

Ultimately, there isn’t a perfect way to limit profiling, something like Invidious or Piped may help. Both have a number of instances, so you can choose one or cycle through them.