I plan on integrating NEAR wallet login in my game, but it’s currently not possible to login to NEAR from itch.io. I wonder if it’s allowed to host the game on a different platform (e.g. 4everland, or Netlify) in addition to itch.io?

Yes, absolutely - we had the same issue last year. Folks generally hosted their games on various platforms, and shared the url in the description here on Itch.

Ps. We have both IPFS and 4Everland as partners (official announcements coming soon), so you can expect some extras in that manner.