I’m not sure to the extent in which they are private, but in my testing they DON’T appear in the following places:

• The “Steam Replay” thing.
• Whatever ProtonDB uses to query your owned games.
• Your recent activity (it also doesn’t also doesn’t count your playtime when displaying the “total time play time” in the last 2 weeks).

Not sure if they are hidden in your owned games list on your profile, but I assume they would be.

Note that the count of games you own (which is public) does seem to include hidden games, if that’s a concern.