I haven't used anything other than Nova on my Pixel 7 Pro since I almost immediately realized I couldn't find a way to turn it off in Pixel Launcher. The whole ad campaign that they ran around personalization was a complete joke, feels like an iClone and I hate it.
Agreed - although, just to check you know about Nova being bought out a few months ago by a firm known for data harvesting? If you did and/or are fine with it no worries. If you didn't, it's worth looking into (and sorry to be the bearer of bad news).
I used Nova for years, but have switched to Total - less slick and user friendly to set up, but very customisable, even more than Nova.
Sadly yes, I've been exploring a few alternatives in case it starts looking like a data mining nightmare but nothing so far, maybe I'll give total a shot
You may be using the default launcher that came with your phone, but if you don't have the search bar, then it's still a 3rd party launcher. Google's launcher forces an immovable search bar on to your home screen.
-Edit-
It's possible this has changed in the years I've been using an alternate launcher. It's been several years since I switched and never really checked back to see if it was still true.
This made me realize that I have a search bar on my home screen that I literally never use and I do use a third party launcher that it could be turned off. Very funny indeed