Why can't I upgrade to Big Sur? I have a 2013 iMac with sufficient space. I am running Catalina 10.15.7

We are your fellow end users so have no special access to Apple reasoning. Apple seldom publishes the "whys and why-nots" of macOS support limitation on older computers.

Disk space has zip to do with OS support. Historically, t is more commonly a video/graphics hardware incompatibility. If we look at the specs of equivalent 2013 and 2014 iMac 27 model. we see that was a different brand and series of video hardware used in supported 2014 iMacs compared to the unsupported 2013 models.

2013: NVIDIA GeForce GT 755M, GeForce GTX 775M, or GeForce GTX 780M

2014: AMD Radeon R9 M290X or Radeon R9 M295X

Similar findings fo the 21.5" models.

As the video hardware in 2012 and newer iMacs is not "slotted" but rather integral with the logic board, not even Apple can upgrade your existing video hardware.

All we can do is talk history. To learn more you need to ask Apple, and they are rather tight-mouthed about internal decisions.

Like mine, your Late 2013 iMac is now on Apple's vintage and obsolete product list, and aside from Apple not providing new operating system upgrades for Macs on this list, they also decided that this iMac also does not provide proper hardware support for Big Sur.

Big Sur will only run on 2014 or newer iMac models. https://support.apple.com/en-us/HT201475