The 2013 Mac Pro only supports HDMI 1.4, so you aren't actually getting 4k at 60Hz from that port.Mac Pro connected with mDP cable to HDMI 2.0. Windows 10 (Bootcamp) shows 4K@60 perfectly. MacOS Monterey shows only 4K@30Hz.
Did anyone have a similar problem?
Yeah, you clearly stated your connection and the screenshot shows that everything is set up correctly and works as intended on Windows.I don't use HDMI on Mac Pro
Display settings in Windows 10 4K@60Hz - Cable mini DisplayPort - HDMI 2.0