The web build was exported incorrectly; the web assembly files should be included.
Aside from that you exported a custom Godot template. I do not know why but I tested the windows build and it just freezes after clicking start.
It is either you broke cross-platform compatibility with your modifications, or it just was intended on your behalf!
If you are compiling from source you can use this Godot guide. but if you are exporting premade official build, it should generate multiple files in the web export path so just include all of them in a single zip file for web, keep an eye on the engine warnings too. And do not forget to name the web export as "index" because itch.io demands the main HTML file to be named "index.html".
Finally, on the game page settings on itch.io mark the web zip file as "playable in browser" then launch it. There is an experimental option for shared data buffer you have to turn it on in the game itch.io page.
This way you would not worry about specific platform issues.
By the way, if you didn't modify the engine source, then I guess you just included the game resources with the exe file on windows. I would suggest to leave game resources in a separate pck file because embedding resources in the exe would change the official Godot signature and falsely flagging it as a virus.
