Just a note: in this case, histones are irrelevant, since prokaryotes don't have any. But more generally, protein binding, modification of bound proteins, and methylation of the DNA itself are all epigenetic mechanisms that could be in play here.

Prokaryotes actually do have histones! Or at least histone-like proteins. https://link.springer.com/article/10.1134/S0003683811060020

To add to the list: activity of restriction enzymes, especially specific ones.

Colistin has a pretty interesting mechanism of action, disrupting ionic balance in cell wall of lipopolysaccharide.

The mechanism of resistance may well be lucky upregulation of ionic balance and cell wall stabilization proteins in response to the attack. Same as for lysozyme.

This kind of ionic environment has wide ranging effects on cell metabolism so changes genre expression. In multiple generations, the resistance might get baked into the genome...

The OP says that the genome sequence hasn't changed. So in order to have that persistent upregulation without any change in the genome sequence, you (most likely) need an epigenetic mechanism to explain it.

> histones are irrelevant, since prokaryotes don't have any

Good point :).