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gypsum isn't breathable at all
I don't think this is correct. Because gypsum is "modern" it gets lumped in with cement renders, plastic paints etc.
However my understanding is that it is breathable, maybe more than lime plaster (variables depending on lime mix). It is also often lower embodied carbon than lime (gypsum is natural and just needs low heating to dry out, unlike lime which needs heating as part of process).
My understanding is the reason it gets in trouble on old solid wall buildings is because it gets damp, the damp stays, and it encourages mould growth. It's a moisture issue but not the one you think. (I think hygroscopic may be the correct word.)
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(I think hygroscopic may be the correct word.)
I know nothing about gypsum's hygroscopic properties, but hygroscopic materials can absorb moisture from the air then release it again. Ideally in an older building this will be over a longer period of time, as this is less likely to cause problems.
I'm currently deep down the rabbit hole of how to insulate an early Edwardian terrace to modern standards without causing damp problems, so in my case I need breathable insulation but ideally it will also be hygroscopic.
For example, if I use mineral wool it is highly vapour open, but has poor hygroscopic and capillarity characteristics. In practice, this means that if it does get wet, it takes a long time to dry out. Plus wet mineral wool will usually sag with the weight of the water (because it's non-hygoscopic, so doesn't absorb it), which will create gaps around the edge where the heat will escape causing condensation on the walls.
This is a problem caused not by lack of breathability, but non-hygoscopic materials, i.e. a moisture issue, but not the one you'd think, so I think this is what you mean @hoefla ?
Flaking is not necessarily damp - it could be efflorescence from the brick.
Fixing what is causing the damp is more important than paint choice though - even a clay / chalk paint is going to mitigate damp a small bit.
The fact that it's a UPVC door suggests that (if it's a solid wall construction), whoever did the last redecoration didn't care for period correct materials, and - I'm going to guess wildly - skimmed everything in gypsum plaster. In which case, paint with hammerite if you care to - the gypsum isn't breathable at all.
To the damp: there's often obvious causes: bad gutters, bad render, breached DPC (can be internal or external), missing caulking, splashback, inadequate drainage / broken drainage.