> Don't they have, in the sense that to keep probing ever more precisely, you need ever more energy, and at some point too much mass~energy in a too small volume is going to form a black hole and you cannot go further ?

This may or may not be true - we can't probe those length scales yet, and maybe ever, so we don't really know - but it has no bearing on ordinary QM, which is nonrelativistic.

> Though this seems related mathematically to how the uncertainty principle can be interpreted through Fourier transforms

Not especially. They're both results in functional analysis, but that's about it.