This will just need an update to the x,y coords of holy mountains in nightmare

This requires decompiling and reverse-engineering the in-engine GetRandomActionWithType and GetRandomAction functions. I did not get very far, since I don't have that much experience with reverse-engineering.
Maybe a more semantic approach through gathering statistics through a lua mod might be a good idea? Then I can get some sense of what goes on inside.
Another idea is to hook the exe and run a lua mod that runs the gen command once, and I can run debugging on it.
Another idea is to reach out to the devs and ask for the falling_everything.pdb that will add lots of mapping to the debugging info.
Even more bold, I can just ask for a description of how these functions work from the devs 😄

I've almost cracked the way these work!

This needs a bit more work. Looks like lua -> ts discrepancy

One thing that I'm worried about is that storing info like that adds expectations about its persistence, and safari, for example, deletes local storage periodically.

One solution is to add accounts and store this in a db, but that will require a db to be available. The current server is stateless and does not have a db, and ideally, I'd like to keep it that way.

If you have any ideas as to how to do this, I'll happily take them into account

Periodically may be more than the user expectation, a small disclaimer could be enough to tone down the expectations, i would not invest in such an implementation unless you go for making lot of users, but this does not look like a project that could interest investors...

I'm not planning for investors ever, and this is more of a passion project that I'm more than willing to spend another $5-10/month on a database.

A disclaimer feels like it would be a solution, but I don't know if that's something I'd be satisfied with.

Then i think you have an answer on the way to go :)
I would suggest authentication only to use the feature then, maybe from some sso

I think this would just add confusion. Since app state is not durable, even browser tab freezing might clear it, making it unreliable at best, and frustrating at least.

It really boils down to why this feature might exist, and what expectations users would have about the feature.

Here, I think that this feature will need a lot of extra code that will need support to make it meet minimal expectations, and also might just add confusion to the usage of everything else

This is a great one! I'll add it to the list of things I really want to add

Hey! What would that be like? I don't have a steam deck

If it has a browser, then it might work