Can you play on any 144hz monitor on xbox series x in 120fps?

If the game allows it, of course

and what do you need hdmi 2.1 for?

Of course you can play on any 144hz monitor, even if the game doesn't support 120hz.

It should of course only have an HDMI connection.

HDMI 2.1 has a higher data throughput rate than HDMI 2.0 or even older versions.

So you can use more functions like 8k, 120hz at 4k, ALLM less input delay or VRR like Freesync, eARC a more powerful version of the audio return channel.

Whether you need, get or even use all of this is another matter.

Especially since most of them are things that only make sense on a TV.