Insulating a shed roof only (Metal Roof, Block Walls)

I'd be inclined to leave it alone. The roof is acting like a dehumidifier.

Ventilation in unheated, unplumbed outdoor buildings is a bit complicated, in my opinion.

Probably worth getting a hygrometer and measuring the humidity in a few different weather conditions

https://www.growshop.ie/product/essentials-digital-min-max-thermo-hygrometer

Ive seen this in a neighbours shed…. spray foam insulation…

clear roof panels on one side…. full apartment built inside … its on Airbnb at 350 per night.

The correct build up of roof should be : Corrugated metal sheeting on 75mm x 50 treated battens on roofing membrane (a.k.a. felt) on heavy duty chicken wire mesh or battens.

Metal roofs will drip under certain climatic conditions even with ventilation, similarly a well insulated building will ''sweat'' under certain conditions so ventilation is important. The OP's shed has a little window with a top ope, if there's a similar ope on the other gable that should supply adequate air circulation.

You could put on some of this stuff
https://nordroofs.ie/product/DEWEB+NTS+Anti-Condensation+Felt
to stop drips, basically it will hold the condensation until it evaporates naturally.

Lots of panels will come it it already installed these days, but you can retro these self-adhesive rolls too.

But wouldn't that result in higher humidity?

I have never seen the membrane installed as you describe but I guess it should work OK as it serves the same principle. Normally heavy gauge chicken wire is put over the rafters (to support the membrane) then 3'' x 2'' treated battens over the membrane. But I note that the design of your roof is somewhat different in that instead of battens laid on rafters you have purlins fitted between the rafters. Perhaps you could fit an extra run of purlins between all the existing ones to support the membrane and use clout nails to tack it on otherwise it may sag.

So the membrane is there to catch the drips rather than prevent them from forming? I think you are either going to end up with puddles in the membrane or the water will run off to a low point and you will have a bigger problem than a few drips.

I would just use the self adhesive membrane on the underside of the metal roof, thats what its for.

Well I would say in an attic the primary purpose is to stop water from getting in, while also being breathable (though attics are or at least should be very well ventilated)

If you are replacing roof sheets then I wouldn't worry about the cost of a couple more m2 of felt tbh.

This use case is exactly what anti condensation felt is for, lots of metal roof panels will come it it pre installed these days, since its such an issue in metal sheds.

Are you on a concrete base and if so, do you know if its has a DPM installed? If not, sealing this might help to reduce the moist thats getting in. If you are not sure, tape a plastic sheet on all 4 sides to the floor and see what it looks like a day later. If its wet underneath then thats where your water is coming from.

Assuming no damp is coming in from the slab…