As a data point, I consistently send game_id as a number whenever it’s relevant (connecting to a game, making moves, etc) and it works fine for me (also in JS). I can’t say whether there’s a bug in how the server handles things when you inconsistently send strings vs numbers, but at least consistently sending it as a number is not problematic.
A different thought: when I was having issues getting moves accepted properly (Debugging WS issues?) two issues turned out to be (a) sending an invalid JWT, which the WS authenticate message gave no feedback on other than not sending me notifications/active games/etc, and (b) a malformed game/connect request, which was silently failing and causing game/move messages to fail because you apparently have to be connected to a game in order to send a move in that game.
The latter issue might explain what’s going on — if you’re connecting to the game in a valid way, but connecting to a string game_id and sending moves to a numeric game_id, that sounds like it could possibly be a cut-and-dry “server bug that you can work around”.