Until recently I used a cheap ($150 USD) Motorola smartphone without a Google account (stock ROM). You don't actually have to log in on Google Android, at least on some devices/versions (this was 11/12). Hope that helps a bit. I actually got an Android (AOSP) dumb/feature phone recently but I have not been able to get Signal to work on that, so I am still dependent my old phone (the aforementioned Motorola) for some things.
If you are in the US (at least), make sure that whatever phone you end up buying and ROM you end up installing (and that specific combination, sigh...) has functioning VoLTE on your carrier or you will be in for an unpleasant surprise.