So here are a few general video’s along with a few interesting papers regarding storing HLW as/in glass-ceramics. The academic research and discussion of this immobilization methods is very robust so lots of stuff you can read on that subject.
BUT we dont have to store Fission HLW if we reprocess it and run it in conjunction with other reactor types like LIFTR. Much of the remaining waste produced in currently operating reactors is still mostly unused and at most 5-10% of the total material is used up. We can pass that through a breeder reactor and convert U238 to P239 which turns “useless” naturally occurring non fissile uranium into fissile plutonium.
So, my point is that assuming we keep using low enrichment uranium to power current BWR/PWR reactors we have an existing solution for the waste (which if ALL of the worlds HLW was combined would not even fill a professional stadium) that easily takes care of all the waste created since we started production.
BUT all that waste is actually fuel if we recycle/reprocess it and we can burn up another large percentage of that waste and its remaining elements are generally shorter lived forms of waste.