“Altered save data” has always referred to all hacked Pokémon (and items, for that matter). However, Game Freak has no real way of telling the difference between a legitimate Pokémon and a hacked Pokémon with possible stats. Historically, they rarely ban players with illegal Pokémon, either (although there have been a handful of ban waves), but I’m not sure how often they issue notices like this, so this could mean they’re going to be cracking down on illegal Pokémon going forward.
Pokémon Home is more closely monitored than your PC boxes in game, since the Pokémon are stored on Game Freak’s servers rather than locally on your Switch. When Pokémon Home first dropped, there were a lot of cases of people bringing hacked Pokémon over from Bank and getting bans. I haven’t heard as much of this recently, so they might have lightened enforcement on this, but there’s no question that Home runs a legitimacy test on all Pokémon that come in. If they decide to be more strict, they’re definitely going to use Pokémon Home to weed out hackers.
If you have illegal Pokémon in your PC boxes in game, then as normal, avoid using them online or release them. Right now, online functions only check the Pokémon you’re trading or battling with, not your whole PC. It’s unlikely this will change unless they add an update to the game.