A couple of thoughts.

I like XPS-based panels with laminate surfaces. They're easier to install and easier to be sure they're watertight. So I'd build a shower room out of such panels in the space available. Either glue them to the limestone or batten to leave a gap if you think that would be better. You'd need to think about how to ventilate the gap. If you really, really want tiles then you could put up tile backer boards instead of the panels. Various materials are available.

I've used such panels on the internal walls in in my wet rooms, but I was a bit nervous about using them over the lime on bales of the external walls, because of the large areas that are involved. So in the one shower that directly impinges on an external wall we mounted a waterproof roller blind on the ceiling. We pull the blind down before using the shower. That's not tenant proof though so may not be relevant for you case.

Tadelakt? Often used in straw bale builds by the type of rich Ecomentalist I aspire to be :-)

Although this will require occasional treatment to maintain its waterproofing qualities. And you cannot clean it with ordinary household products, so probably not best for rented accommodation.

I've seen Tadalakt used effectively in a shower cubicle against a stone wall that had an initial layer of sprayed cork insulation applied.

The company I work for doesn't recommend wood fibre insulation for the bathroom environment, but, when it is used, we suggest using a moisture-resistant plasterboard and batten approach (flexible woodfibre between battens) and using a moisture vapour-variable membrane, (Pro Clima Intello et al) carefully taped and sealed.

I'd still use an insulated tile backer board for the shower cubicle itself and make damn sure the bathroom is adequately ventilated and the wall exterior has a breathable finish