Chromium now has initial, experimental support for the xdg-session-management #wayland protocol, which will start shipping in canary channel in the coming days. I've implemented and tested it against Mutter 48, the only compositor supporting it atm - also experimentally - since version 47.
Quick demo at https://youtu.be/OG9ZLXzlwkQ
Setup instructions, known issues as well as a bunch of design notes can be found at https://notes.nickdiego.dev/chromium/wayland-session-management on which I'll base a more structured blog post, to be published soon.