FYI, as I googled my issue for hours:

If you face issues with the second USB-C/Thunderbolt port not working, and you are not using docking station:

Disable in BIOS: "Type-C Dock Override".

In my case when the first USB-C/Thunderbolt port was connected to the AC, and the second USB-C/Thunderbolt port to the monitor, it were not working simultaneously. After disabling this setting, it is now working as expected.