Great question — answering as the UphillTech team:
The brass device you show is a shutoff valve, with the end cap just unscrewing to reveal the shank that needs turning which will have a slot for a screwdriver and/or a square end. The "standard" system in Switzerland (and I live here so I have worked with these valves and replaced two a couple of weeks ago), will have the same pressure for hot and cold. If the hot is worse than the cold then there is a restriction of some sort somewhere. This could be a washer that is too squashed and occluding the pipe, or there could be a small mesh filter in one end of that stainless flexible pipe that you show. Given that you state that the flow is good on the 4th floor, then that does limit what needs...
Full answer by Solar Mike: https://diy.stackexchange.com/a/331965 (CC BY-SA 4.0).
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