could i connect my Xbox to my iMac using an adapter??

No. Even if your iMac were one of the few models that support target display mode your sig says you’re running Mac OS 10.15 which does not support it Use your iMac as a display with target display mode - Apple Support

Furtehrmore TDM was designed to be Mac to Mac only.

Only a few older Macs of those that supported Target Display Mode could actually do that, and it required an external device, the Kanex XD to support the HDMI output from the XBOX as a video source for the iMac. Long out of production those are hard to find, and the iMacs that worked with it were like from 27" models from 2010.

If you want to try using your local network, WiFi works with some lag, but performance is better if you have wired Ethernet for the iMac and XBOX, check out the OneCast app for Mac.

https://onecast.me/