If you look here:
Mac computers can use an HDMI cable or adapter to connect to a TV, display, or other HDMI device.
support.apple.com
It says that "MacBook Pro introduced in 2021 or later" only supports up to 4K up to 60Hz. To get up to 4K at 240Hz requires M2 Pro.
I agree the wording is somewhat ambiguous (it doesn't really say whether or not lower resolutions will get higher refresh rates) but I think we could probably assume that it is not guaranteed, if it works on a particular setup that's great (for example on my M2 Mac Mini I get 75Hz on my 1440p display) but Apple doesn't promise it.