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.
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I ended up with a $100 Pixel 5 that I loaded IodeOS on and stripped everything out but phone, messages, Signal, settings, and contacts. I'm using Before launcher to make it as simple as possible.
The pleasant surprise is the battery has 1200 charge cycles on it, and I worried it would need replacement...but with so few processes running, I'm getting 7 days of battery life on a 6-year old phone.
It's still too big, but it was the smallest thing I could find that was guaranteed to 100% work with a Lineage fork.