You can get battles in the Old Shark Room [ https://play.pokemonshowdown.com/oldshark
], which is a private room in PS!. It mostly focuses on Older Gens of Hackmons, but Galar PH is also played there.
Or you can try the Other Metas Room [ https://play.pokemonshowdown.com/othermetagames
] too, but the userbase there doesn't give a tad about PH lol.
Sometimes, the Tournaments and Tours Plaza Rooms conduct some RoomTours, so you can join those rooms as well.
It also recently got an LCoTM Ladder, and also got one in the past. You can wait some months to get a ladder for it again.