Question about HP M34d

Unfortunately, I can't answer this question because my notebook and the screen are from HP.

No difference whatever the type of connection

I would not have noticed that. Depending on which device I connect to it (HP Elitedesk / DP or HP Elitebook / USB-C), the monitor switches between 60 or 100 Hz without any problems.

Not that I know or have noticed. I have an HP Spectre Win11 Pro connected via UBC-C and alternately a MacBook Air 2022 ... Works fine with the included USB-C cable (which also charges, which I find super handy.... only one cable ready). With MacBook Air and Pro this is not self-evident, because with most monitors (Dell, ASUS) the connection does not work via HDMI /USBC adapter cable ... only via original adapters from Apple.

I have a similar situation in my home office. Home computer on HDMI and business laptop (but Windows PC) on USB-C. I wouldn't have noticed anything wrong with the refresh rate.