Using iMac mid 2011 as a second monitor for my macbook pro

I am tryong ti use my old iMac 27" Mid 2011 (macOS 10.13.6 High Sierra) as a monitor for my new MacBook Air 2020 M1/16/1000 (macOS Big Sur 11.2.3) laptop.

I found this in an earlier thread:

Also the 2018 MacBook Air may not work, if it has been upgraded to Mojave or Catalina.

Indeed, It has us confused!

It is the iMac used as a display that is constrained to no higher OS than 10.13, NOT the SOURCE computer. Catalina still supports TDM on pre-2020 Macs.

Recent success report with steps for TDM and Catalina here.

https://discussions.apple.com/thread/251899135?answerId=253627813022&page=1

Apparently it's not the whole story ... I can connect to the 27" iMac even though they say it's not possible. However, I only get screen doubling. I can't use the fullscreen of the iMac. Så I literallyjust get the same size as the 13" monitor from the laptop, and then -why bother?

Is there a workaround so I can use the fullscreen-size?

Or a recommended monitor that doesn't cost the blue out of the sky?