We used Godot 4.1 on our game and exported a web version + desktop platforms: Windows, Linux Mac so it's definitely doable! :)
Here's how for the web version:
You need to configure your export presets for the web version, name your "executable" file index.html so itch recognizes it, zip the whole exported web folder, upload it on itch, choose "This file will be played in the browser" and then you have to enable ShareBufferArray support on itch as well so you don't have errors while launching the game. (It's a box to check)
Note: I don't think we're allowed to upload anything during the vote period!
EDIT: Typos