I attempted to write
Of course, you may be subject to other ordinances outside city limits, however most townships and cities within this county have adopted similar rules.
but grammarly suggested I add a comma after however:
Of course, you may be subject to other ordinances outside city limits, however, most townships and cities within this county have adopted similar rules.
Is it required(or simply good practice) to have a comma after "however" when used this way, and if so what is the rule I need to understand? It feels more natural to leave it out, though I suspect that's an artifact of conversational English where commas are equated with pauses. In the sentence preceding this one, though, I could have used "however" or "but" in place of "though" and in neither case is a comma suggested after the word. And yet in the sentence preceding this one, "though" requires a comma after it - and that one feels correct!