Display problems

You are fighting far more than cables here.

It appears that pre-2020 Macs that could be the source for Target Display Mode will no longer work if upgraded to Big Sur.

The support article on Target Display Mode has been archived and is not clearly written. The short and sweet version of hardware requirements:

VIDEO SOURCE COMPUTER (the one sending the video signal to an external monitor):

An Intel Mac running macOS 10.15 Catalina or older. M1 Macs and Big Sur mac OS11 are not supported.

TARGET COMPUTER (the one to be an external monitor):

An iMac 27-inch (Late 2009 and Mid 2010), or any iMac from 2011 to Mid 2014. The target computer must be running OS 10.13.X High Sierra or older.

Target display mode requires macOS High Sierra or earlier on the iMac used as the external display. It does not work with macOS Mojave or later.

I gave up attempting target display mode with my 27 inch Late-2013 iMac with the correct cables and operating system versions. Now, I use Apple's built-in Virtual Network Computing (VNC) to share another Mac screen onto the iMac, though less so these days, as it has been replaced with a new M1 mini and 32 in 4K display.