Just after creating a new project in Itch.io, you only need to fill/enable 3 options to make this playable on browser:

Kind of project:	Select HTML.
Upload Files:	Be sure to upload a .zip file, if this is generated via Unity it will already have the needed index.html file to play on browser.
Enable option:	“This will be played in the browser”.

That’s it!

Always test this built both locally and in Itch.io website, as with newer Unity versions (2020+) there may be some problems based on the engine compression. You may see the game not loading locally, but actually loading through Itch.io browser. If you see the following error:

both async and sync fetching of the wasm failed

Here’s how to fix it:

Go to Unity > File > Build Settings > Player Settings > Compression.

Option 1) There disable Compression, and enable Decompression Fallback.

Option 2) If the previous doesn’t work, select GZIP compression and enable Decompression Fallback.