My internet is fine (cabled fiber) and has always been fine. But as soon as it is a crossplay game, I.e. one team on each type of console, the quality of the gameplay goes far south. The next game with just the same console is fine again. Seeing this pattern over several games makes me draw the conclusion that crossplay is not up to speed yet. Almost all games were ok the season before so crossplay does not improve the experience at all. Of course it was the random laggy match here and there but not as systematic.

No. It's P2P. If the host has shitty internet, everyone's connection is dog water. Cross console play makes it lag even more.