Insulating the sloping ceilings of the upper floor from the attic

Good day I rent in a very old house with a cold roof. The upper floor extends into the roof and has a roof slope of 2.5m length on both sides of the house. From the attic, I can see into the gaps between the rafters (100mm) up to the exterior wall. Considering the rising energy costs, I am thinking about what could be done with low cost and effort. I do not yet know if the landlord will contribute. In my opinion, pulling a vapor barrier is hardly possible due to the described situation. I could cut EPS boards and slide them down or insert mineral wool in rolls. The insulation lies directly under the tiles. With mineral wool, I see problems with moisture and with EPS, that the boards do not properly close against the rafters. Are there alternatives? What would be the lesser evil? I know that my considerations are far from an ideal insulation and roof structure. It's about saving some energy for the next 5 years. Thanks for all suggestions Remo

Have you ever looked into loose-fill insulation or blown-in insulation? There might also be solutions that do not require a vapor barrier.

You are a tenant and need the landlord's consent for something like that. For damages caused by improper execution... keyword mold... you are responsible and your landlord will hold you liable.

Especially with thermal insulation on old buildings, so much can go terribly and especially terribly wrong. Stay away from it. Your landlord should hire a professional. If they mess up, at least it is not your problem.

thanks WilderSueden, I looked at what is available. It would of course be practical to accomplish. However, I would then have material up to the bricks. But as an alternative, a good suggestion. @MisterD. I write that I don’t know if my landlord will contribute to the costs... so I intend to talk to him. (I did, he covers the costs... of course not for reroofing or similar) To avoid mistakes I am gathering information..(among other places here) and hope for professionals who give me good advice

(I did that, he is covering the costs.... of course not for re-roofing or anything similar)
To avoid mistakes, I inform myself...(among other places here) and hope for experts who give me good advice

Then avoid the mistake of inserting yourself here as the client (and contact person for damages) between the landlord and the contractor. Don’t just let him cover the costs, but the whole thing at once. Making yourself useful in obtaining estimates should be the only thing you have to do with it. He also nicely has something to deduct with the craftsman's labor costs, which you couldn’t really make good use of.