I have similar issue. But its possible to turn off notification in the app. I used the classic app a long time. But now im using the new one. Go to the settings.
Muting a player

The OP mentioned that the opponent is sending PMs and wants them to stop. Unless PM was a chat message.
If it is a PM, turning off notifications may help a little.
I am participating in a tournament with 3 days/move time control. One player keeps PMing me "go" immediately or shortly after making a move. Fine, I may take a day or even two to keep up with my games at times, but that should still be fine in a 3 days/move game. So I tried disabling chat in that game. But I still keep getting notifications on my phone whenever he urges me to "go". Also, in the game I get a new message notification, although when I click on it I only get a message that chat is disabled. So how do I block these messages? Do I need to block the user entirely? If so, how will this affect the rest of the game?