Can I play multiplayer Team Sonic Racing across platforms?

Unfortunately, Team Sonic Racing does not support cross-play, which means you can not play Team Sonic Racing across other platforms.

This was confirmed in an interview with Takashi Iizuka, the lead producer and current Vice President of Product Development for the Sonic the Hedgehog series at Sega.

Interviewee: "Will you be supporting cross-platform play? Because it's on four platforms, correct? So will you be able to matchmake with people across platforms?"

Takashi Iizuka: "Since we're not quite at the point where we can get all platforms to play together in one unique universe, we're kind of moving away from focusing on getting that on cross-platform play." Team Sonic Racing - Developer Interview