Don't pay too much attention to me because I'm not a web developer.
But what I understand.
In order to use the "SharedArrayBuffer" it is necessary to configure certain headers on the server side, to prevent external services from accessing the Buffer and stealing information.
The problem is that the game can only run if it is on that server, in this case on Itch.io.
If you need to access the game from another server (not a client, but an iframe), I understand that your own external website. It is necessary to configure "Cross Origin Isolation" in order to avoid any attack that could steal information from the buffer.
How to configure "Cross Origin Isolation"?
I do not have the slightest idea. But it is something that must be done at the server level, that is, not the programming of your game, but on the server where your website is and/or in Itch.