It's indeed a miniature Crassula and does look like a hybrid and could very well be as you say (I remember it differently but ICBW).

Sure, it could be repotted into a slightly larger pot in porous mix, but be aware that Crassula do most of their growing in the cooler parts of the year.

It looks like Crassula 'Ivory Pagoda', a very nice plant. It's not the most common Crassula but not anywhere near as rare as 'Buddha's Temple' which I once had in my grasp and regretfully did not buy.

I've had a few of the 'Ivory Pagodas' and killed the first one with too much sun. It will appreciate a few hours of morning sun and mostly shade the rest of the time. There's no rush to repot it, maybe let it acclimate to a good spot first.

Thanks so much!