Roof insulation polyurethane PU rigid foam 100mm thick

Hello everyone,
I urgently need tips and advice on the topic of roof insulation.
We plan to have our roof renewed next year. Now it’s about the roof insulation. Our roofer recommended the following:
Polyurethane PU rigid foam 100mm thick // Type: puren Protect N 023.
That would be an over-rafter insulation. Now I read in forums etc. that the sound insulation with this type of insulation is significantly lacking. The noise level is sometimes very high. On the one hand due to the boards themselves (as they apparently expand during the day and contract again at night) and the boards themselves do not have GOOD sound insulation.
We would quite like it to be more bearable under the roof in summer and of course also quieter (or at least that one can endure the noise level) from outside.
Can you give us tips on the best way to insulate such a roof??? Is there anyone who has experience with this type: puren Protect N 023?
Please help... THANK YOU!!!
Best regards Anke

I think that with intermediate insulation of cavity insulation wool the soundproofing would be better, but the efficiency of the PU panels on rafters is higher.

Hello Nordlys,
Thank you very much for your contribution.
Hmm, so in our case would you have these PU boards installed and additionally (for soundproofing) also install this insulation between the rafters? I'm totally uncertain now. You spend a lot of money and in the end, you want it to be good. Many complain about these PU boards...
-in summer it would still be very hot and on top of that, the soundproofing is really bad.

I see how companies here build new houses whose attic is supposed to be inhabited. They use insulation between rafters and under rafters with glass wool. K.

Counter-rafter insulation? So rather not the above-rafter insulation???

This is how they do it here in new buildings. Team massiv, Specht, ECO, and others. I am not a carpenter, I only see what I see and they have inter-rafter insulation fleece, and it is quite quiet up there, but our attic is used as a basement, not inhabited. It also stays reasonably cool in summer. Reasonably, that is, not like downstairs.