For this particular situation, I would lean towards a properly fitted blackout curtain and pelmet system, mainly because your windows tilt inwards and because near-total darkness appears to be the first priority.
Solid internal shutters can provide excellent thermal performance when they fit closely against the frame. Traditional shutters worked particularly well because the shutters, folding pockets and window reveals were designed as one system. Retrofitting them to modern tilt-in windows is more difficult. The panels need somewhere to fold, they may interfere with handles or the inward swing of the window, and you would need to open the shutters before opening the window.
A curtain system would be more forgiving and easier to alter later. However, the details matter more than the thickness of the fabric alone. I would use:
a wall-mounted box pelmet that closes the gap above the curtain;
a track wider than the window opening;
curtains that return towards the wall at both ends;
floor-length or sill-sealing curtains;
generous overlap where two curtain panels meet; and
a separate blackout lining or tightly woven blockout fabric.
The aim is to create a reasonably still pocket of air between the glass and the curtain. A pelmet helps prevent warm room air from dropping behind the curtain, cooling against the glass and returning to the room. Government passive-design guidance similarly recommends snug curtains, sealed edges and pelmets rather than relying on heavy fabric alone.
For severe light pollution, the weak points will probably be the perimeter rather than the curtain fabric. Side returns, overlapping centre panels and a close fit at the bottom may be enough. Small magnetic tabs, removable side channels or hook-and-loop strips could also control the remaining edge leakage without creating a permanently sealed installation.
Solid shutters may still outperform curtains thermally when they are well fitted. Historic Environment Scotland recommends using existing timber shutters at night and identifies draught-proofing as the first priority for reducing heat loss through traditional windows. However, shutters with adjustable louvres are different from the traditional solid-panel shutters in your museum photos. They provide excellent privacy and adjustable light control, but small gaps around the panels and louvres mean they should not be treated as true blackout coverings. This guide to PVC plantation shutters
https://iseekblinds.com.au/blog/complete-guide-to-pvc-plantation-shutters explains that distinction and the normal sources of light gaps. For transparency, I am associated with iSeekBlinds, which published that guide.
Condensation is the point where I would be cautious with either option. Once a curtain or shutter insulates the room from the window, less indoor heat reaches the glass. The glass can therefore become colder, which may increase condensation behind the covering if indoor humidity is high. Neither system removes moisture from the room. Keep trickle vents and required ventilation paths open, open the curtains or shutters during the day, and check the glass and frame regularly during the first winter.
Before committing to joinery, I would test one room with a temporary system. Hang an inexpensive blackout curtain wider than the opening, add a temporary cardboard or plywood pelmet, and block the side gaps temporarily. That should reveal how much darkness and comfort you can achieve. You could also compare the window and room-side temperatures with an infrared thermometer on similar cold nights.
My overall comparison would be:
Solid shutters: potentially better insulation, durable, easy to wipe clean and architecturally attractive, but more expensive and complicated around inward-opening windows.
Blackout curtains with a sealed pelmet: easier to make, easier to modify, likely better for near-total darkness and more compatible with seasonal ventilation, but only thermally effective when the top, sides and bottom fit closely.
For your windows, I would try the curtain and pelmet system first. If it does not provide enough thermal improvement, removable internal secondary glazing behind the curtains may deliver a greater benefit than replacing the curtains with retrofit shutters.
