You should be hanging the washing outside!

If you do fit an MVHR unit in the bathroom, you don't have to worry about buffering moisture, which is an odd concept anyway.

I've read they can be noisy too?

We dried washing in a utility room for a while - when the weather was not good enough to dry outside. It did dry the washing but long term caused mould problems and we stopped it. Best thing we did was to get a separate spin drier, it will remove a lot more water than most washing machines Caveat, it is time consuming in that you need to divide washing into 3 or 4 loads and may be spin each one for 3-5 mins.

I’m no expert, but why try to buffer humidity? Wouldn’t it be better to completely tile the bathroom, then the water vapour has to be visible and trapped on the tiles. Either ventilate by opening the window or use a de-humidifier?

What is your thinking behind buffering (storing water in plaster) with MVHR Ed?
Just seems an odd thing to do to me. Not experience (other than a dry house and having lived in damp ones).

Thought it might be.
I weighed some washing before and after drying.
A typical load of my washing held 1.9 kg of water
Fancy running your numbers again on my washing. I usually take it out several hours after it has finished, so would normally be at ambient temperature.

100 m² roughly-cubic 2 storey house might have 400 m² of indoor walls and ceilings. Don't know numbers for clay so assume equivalent of 10 mm of wood on those surfaces. The floors might be wood too but would probably be well-enough sealed to not to play in this game.

Total mass of wood might be 400 m² * 0.01 m * 400 kg/m³ = 1600 kg.

From the table here: http://www.csgnetwork.com/emctablecalc.html

equilibrium moisture content, at sensible temperatures, 40% RH would be 7.7% and at 65% RH would be 12% so a change of 4.3% which would be 68.8 kg.

Compare that with 1.9 kg from your washing (which could be less with a spin drier, I expect).

Wood, even through the end grain, would be too slow to help for short peaks like this, I suspect. Clay might be a lot better - I don't know.

Latent heat of condensation of water, at around room temperature, is about 2450 kJ/kg so the condensation of 68.8 kg of water (say starting from a house dried out as far as practical in the autumn and allowing the moisture content to build up over the winter) would release 168.56 MJ or 46.82 kWh, 0.4682 kWh/m² so a bit less than 1/30th of Passivhaus heating requirements.