I really can't see how the presence of GA on a site would invite impaired SERP performance, it wouldn't really work as an incentive for people to use it would it? Mind you with GA4 Google seems to be actively making their product even shitter.
Google is already tracking everything without the need of GA on your site,
It could be the case if your website have shitty UX (high bounce rate, low in time page, etc...) and you provided more accurate access for them to take into account
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