Update 0.157.1 is currently rolling out. PvP should work again!
The remote PvP invite does not arrive at this moment.
But there is some workaround. Although not ideal. Battle through QR scanning does still work. Although it is not clear if scanning a friends QR using a picture on a secondary device works on a remote battle. [Now Confirmed]
If you are on an older version than 0.157.0, hold on, don’t update. Niantic is aware and promised the fix in the next version. I guess 0.157.1.