What is the lifespan of iMac (21.5-inch, Late 2013)? Running macOS Catalina V 10.15.7.

As Jeffrey pointed out, you have the latest MacOS that runs on that model.

Apple provides parts and service for 5 years after Apple last was selling a product.

Additional support can sometimes be obtained for up to 7 years, at which point Apple considers it "obsolete."

So I think you can see that computers might be expected to last ~ 7 years or so.

My employer "replenishes" all our work computers after 3 years, it is mandated. They are considered not reliable to my employer at that point.

That said, I had a 2008 iMac that worked fine up until a few months ago when the power supply failed and the unit was then recycled.

I have 2010 and 2013 MacBook Airs that still are running, and a 2015 iMac that is running.

I would guess that a 2013 iMac is probably getting near end of life and you should always have at least two reliable backups for when that happens. iMacs, like laptops, are very compressed in space and some areas will get quite hot while operating normally. This temperature cycling can ultimately cause the wear and tear on electronics that causes it to wear out.

sorry, no. that Mac can only go as far as Catalina. but if it still does what you use it for, you can keep using it.