I've got a late 2013 iMac (
iMac 14,1 2.7GHz) and it's running Catalina. Mojave ran smoother IMO, so I'm disappointed that it won't be updated with Big Sur.
Actually, looking further into it, as far as 2013 iMacs being incompatible with Big Sur goes, I think it comes down to the minimum requirement of 1.5 GB of Graphics Memory (which the MacBook Airs and MacBook Pros from mid/late 2013 adhere to). Although my own entry level 21.5" late 2013 iMac physically meets this requirement (due to Integrated Graphics w/1.5 GB from shared memory) the higher end 21.5" and lower end 27" models with dedicated GPUs only have 1 GB of Graphics memory.
This might explain why the DVD player app appears to have problems loading on the 2013 iMac with the dedicated GT 750M chip when running
this particular macOS Big Sur patch.
Perhaps as a result of not wanting customers who purchased the 2013 iMacs with 1 GB graphics memory to feel
ripped off, Apple went out of its way to ensure that the other 2013 iMacs would also not be supported to alleviate customer confusion or frustration but kept the basic mid 2014 21.5" model supported.
These days, Apple has become less transparent as to why older Macs are dropped from macOS updates than in the past.