Aside: The links to the web game in the post don't lead to being able to play.
but I do wonder if BEAM is a bit of an overkill, even fly.io (known among developer threads to be very unreliable uptime) wouldn't be my first pick.
Cloudflare Durable Objects really is generous, not often can you get replicated database and realtime sync for such low barrier in cost and implementation.
I do wonder tho what Cloudflare's ultimate game is, as I'd imagine once they corner the market and practically everything is running off it, wouldn't be hard to say raise the $5/month to something higher.