i am only dabbling in this space myself, so can't answer everything. all the formats i mentioned are for a quantized version of the original model. basically a lower resolution version, with the associated precision loss. e.g. original model weights are in f16, the gptq version is in int4. a big difference in size but often an acceptable loss of quality. using quants is basically a tradeoff between quality and "can i run it?".
examples of original models are llama(2), mistral, xwin. they are not directly related to any quantized versions. quants are mostly done by third parties (e.g. thebloke[1]).
using a full model for inference requires pretty beefy hardware. most inference on consumer hardware is done with quantized versions for that reason.
there are modern products in this niche, and there is huge interest. the market certainly seems to be there (regium tried to defraud people for almost a million dollars i believe was the kickstarter sum before they got shut down).
there is squareoff [0], with new products currently in development (swap / neo)
then there was regium, an elaborate scam on kickstarter [1]
now there is phantom [2], which hopefully is not a scam. they at least posted some engineering details on hackaday [3]
squareoff has chess.com support, hopefully with lichess support coming (they are promising it, but has not yet happend). phantom claims working lichess support and to work on chess.com support
If you are paranoid about something like this happening, just use https://www.qubes-os.org/. all usb devices are jailed in a non-networked vm by default.
In general, if what you do warrants that level of paranoia, qubes will help you massively.
since the qr code is just the totp seed, i simply print the seed in huge font on a sheet of paper. chance of enough degredation to inlegibility is pretty slim if stored correctly
examples of original models are llama(2), mistral, xwin. they are not directly related to any quantized versions. quants are mostly done by third parties (e.g. thebloke[1]).
using a full model for inference requires pretty beefy hardware. most inference on consumer hardware is done with quantized versions for that reason.
[1] https://huggingface.co/TheBloke