I've used Matomo https://matomo.org/ before.
There is a cost, but it's free if you host it on your servers, which also requires setting up.
BUT
If it's a WPX hosted website then you know their SiteSupport will do it for you (speak to WPX sitesupport BEFOREHAND).
Clarity https://clarity.microsoft.com/ is another option I've seen, but not personally used.
And my first ever analytics tool (about 16 years ago) was Statcounter https://statcounter.com/ but I haven't used them for over 12 years now, so no idea what they're like.
And here's a list of some more, some paid, some free (again, I've never used any of these, so no idea what they're like)
https://searchengineland.com/google-analytics-4-alternatives-free-low-cost-428794
The only other thing I'd take into consideration is that the main reason you're looking to do this is to "hide from Google".
However, if your website has been "hit" in recent updates and you're literally getting ZERO traffic from Google (or less than an average of ONE click per ONE article published on your website), does it really matter whether you "hide" from Google or not?
If Google has "killed" your website in terms of Google rankings already, they can't make it any worse!
That being said, I will definitely be doing this for new websites...
PLUS
Has anyone yet in the ENTIRE UNIVERSE (yes, I going further than just Earth) actually worked out how the %$£& to use GA4 effectively??? 🤣🤣🤣🤣🤣🤣🤣