Do you know yourself for a fact that no data is being taken by Sync itself?
And its a fact that Google and Firebase are taking your data. Even if Sync itself doesn't collect any data, it uses Google products (as stated in their Privacy Policy which I'm 1000% you did read), and any and all google products will take your data.
That's the point of using a FOSS client, if it collected data people would know, the code is public. And the data collection can be removed, since the code is public.
Even outside of data collection or privacy, which clearly you don't care about, we should avoid giving Google more power. Look at manifest v3 or the web integrity API. That affects not only your privacy, but your security and ability to use the internet. And not only yours, but the whole world