You should add some kind of almanac (not the deck menu type) that's basically an almanac of all stones from 1 to 100, the special stones (negative 1, 0, x, mirrorstone) and the tools plus maybe some the stones after 100.
The almanac should also have some kind of unlock-to-view thing. I'd say that all non-composite stones get unlocked in the almanac when you get them (e.g. you can view 13 in the almanac when you beat the 13-prime master) and composite stones get unlocked when you craft them. (e.g. you can view 6 after you create the 6-gem, by merging a 2 and 3 gem together)
slight visual bug?
Save data is saved in the path "idbfs/Strategems". Maybe you have high-privacy browser settings set to wipe this data when closing your browser? Have other browser-based Unity games been saving fine for you?
(For me, using a Private Window in Firefox results in new save files which last for only that window, so it may be something similar to that.)