Sorry it took me a while to respond. It turns out the game id is a feature that I only experimentally tested out on my machine, but never fully implemented, sorry >.< The "different games sharing the same save data" is a problem I have been aware of, but my brain remembered me fixing it, when in reality the version on itch still has this problem. So the save data problem is 100% a bug, I will try to fix it soon!
The upgrade coming from gameName.html makes sense, this file contains a lot of generated code (I'm using a web framework called svelte), and the upgrade funtion comes from the framework, not from me. The exported file is really not meant to be edited directly. If you really need to change things there, the section of the html within the <script type="gamedata>..</script> tag contains the entire game, the rest is just the engine.
That being said, there should be a place in the html thats says:
const NAME = "trash_engine";
const STORE_NAME_RESOURCES = "game_data";
Changing any of these strings to something else might work, but I haven't really tested it.