C922x

I record using a brio500 (i mainly chose it because of the design and the neat physical privacy shutter tbh, it's not that great of a camera) The logitech one you wishlisted is probably fine, the other ones too, they probably won't be as good as your phone (most webcams in the sane pricerange aren't) but one thing I recommend is going into lighting, as even a small keylight or something that elevates you from the background does wonders for better tracking. :)

other comments have pretty much told you what you’re looking for here, basically the no name amazon brands are really untrustworthy, so if you actually get the specs theyre advertising you would be pretty lucky. i have a recc for a mid range cam for you, the logitech c922 pro cam is pretty decent at least by my standards. i got it half price for about $50 AUD a couple years ago, so for the price point its good quality, havent had any issues apart from sometimes colours/skin looking a little washed out (though i am sure theres a way for me to fix it, just havent looked into it yet) autofocus is honestly by my standards great for a cam this price too be sure to research further yourself to see if you like ir though, good luck 🤞

I have a 922 Pro, it's 1080p30, so not a 60 fps cam if you need to be in 1080p. I also hate it, it's hard to get the colors right, even in good light. For now I am only using it as a top down cam, and not my main cam. For my main can I use an Elgato Facecam MK.2. And that is a 1080p60 cam, and the colors are much better. But to be honest, for a relatively cheap, and good webcam, with 4k30/1080p/60, I would have a look at the OBSBOT Meet 2. You can also get the OBSBOT Meet SE, at 1080p/100fps if you don't need the 4k resolution, for an even cheaper price.

I have a Logitech C922 Pro which works quite well & a cheap AliExpress endoscope camera to watch the nozzle.

A third for C920/C922. Been using them for years. They are fantastic.