I had this issue too, it was resolved by increasing the vm.max_map_count. This link explains how to modify the value better than I can:
Solutions for common crashes you may run into while playing A Hat in Time on a Linux system through Steam Play....
steamcommunity.com
After increasing the max memory mapped regions available I've finished the tutorial and played several matches without crashing. For reference, I'm on Linux Mint 21.3 running the 555 Nvidia drivers. Maybe you're hitting the same problem?