I don't consider Google to be a data privacy respecting company, rather the opposite of that. Probably the last thing I would trust is a Password Manager from Google.

You can alway use Keepass or variants of it and sync the database in encrypted form to some cloud storage or your own webspace, hosted on a small Raspi or something similar. There are privacy friendly and safe ways, if you care to find, understand and implement them. Of course, I'm aware that some computer knowledge is required for this. IT noobs will certainly struggle.