To get a PC display to become active, you set its resolution arbitrarily, and hope nothing blows up from setting it too high.
to get a Mac display to become active, you need the Mac to query the display, and the display to answer with its name and capabilities.
Th reason your Mac will not go higher by itself, is that HDMI 1.4 is inadequate to drive that display with one cable, so the resolution reported over HDMI is the resolution for FIRST of the TWO HDMI 1.4 cables you will need to connect to drive that display in two halves, using Picture-by-Picture in the display and macOS Extended Desktop in the Mac to put it back together.
Take Sonicray's advice and use DisplayPort, DisplayPort over USB-C, or DisplaysPort over ThunderBolt (if so equipped).