On the 52' (a Moody, lovely boat) the windlass was on the engine batteries.
I never used it without the engine running. I could have... in fact, for brief moments, like adjusting chain tension, I did...but not for full anchor jobs, never.
I never had a bow thruster, but it stands to reason that one wouldn't use that without the engine running (and alternator charging) either, so that should just go on the engine starter too, right? Which can be a simple automotive starter - cheap. It never deep-cycles, does it?