You can’t get doxxed from just your IP, that’s a bunch of internet bunk. The most they can do is figure out the general area that your ISP is based in, and sometimes that even points to another city entirely. They’d need a lot more info from varying sources in order to actually dox you.
My own IP’s been in the open for a decent while now, and I’m fairly active in quite a few discords, with my server’s being open to the public and all that (though it doesn’t get that much traffic tbh). If someone disliked me enough to try and DDOS me, they wouldn’t need to look far to find the IP, and I’m not too worried.
I work with some streamers who get DDOSed a decent bit, and if you stick to your guns and laugh it off, they don’t tend to come back.
Though back on topic:
Since sleep mode is working in your local network, I’d wager there’s just something weird enough with playit.gg’s tunneling implementation to prevent the initial connections/pings from getting through properly. (and if that’s the case it’s out of AMP’s hands)
Though agreed, if someone has found a solution to the problem before, it would be nice to know in case someone else runs across the issue.