Central computer with terminals in the rooms

Couldn't you use a soundproof rack? Or in the room next door? Even powerful computers can be made quiet. You don't need a gaming PC. With SSDs, large slow-spinning fans it will already be quite noiseless.

Liquid cooling should reduce the noise level to nearly 0.

I know it from my employer's office that all PCs are located in one room and everyone accesses the VM only through a terminal. Everyone has different screens and full performance and resolution. And no PCs and no noise in the office. That is exactly what I wanted at home as well.

Then just take the solution from the office?

Yes, I will take a look at it later.

I thought there might be people here who already have such a solution and can give recommendations.

Apparently, I am alone here with this idea.
I don’t know why almost everyone finds it so absurd to banish all PCs to one room to avoid noise and have everything neatly centralized...

My two servers + NAS are in the rack and it is located far away from the desk. Under the desk is a PC with a (amateurishly) soundproofed case, on the desk 3x 27". No problem, the controlled residential ventilation is louder. I consider making such a fuss pointless (although everyone has to clarify sense and nonsense for themselves), or in other words: It has zero advantages for home. Children or others will tend to work with laptops anyway, which you can hardly if at all hear.

Apart from that: What do you personally do with 4 PCs for daily work? That sounds more like a poorly thought-out concept.

Same here. I see no problems with PCs in the study, even with multiple monitors and server, NAS, etc. elsewhere, you can still access everything you need from the sofa with the laptop.

But if you want to do it, then just do it.