How do I get game mode to work on HDMI 2/3 on the 43E78QTUK?

I’ve just bought a 43E78QTUK TV which has the game mode but it only seems to be an option on HDMI 1 which runs at 60hz only and I want to play ps5 games at 120hz.

I’ve tried watching YouTube videos on similar TV’s but I can’t get the game mode to work on the 144hz HDMI ports and the game menu shows 60hz when in game.

I’ve made sure my ps5 settings allow 120hz and have changed the HDMI format to 144hz so why can’t I switch on the game mode/ play games at 120hz? Thanks for all suggestions