Apple ceases regular "features/fixes/security" type updates after the third new OS version, and they release new OS versions every year now, so that's three years. If a security problem is severe enough, they often bring out an update for a no-longer-routinely updated but fairly recent system versions.
Apple drops support for older hardware as well, though this typically goes back far longer than three years; typically about six-to-nine years, and occasionally longer. As I often say, the day your Mac cannot update to the latest version of macOS starts a three-year clock in which you should update the hardware to something newer (doesn't have to be brand new, but more recent) in order to prevent becoming vulnerable online.
Your late 2013 is nine years old AND Catalina is the last supported OS version for it, so you're experiencing the double whammy. Time for a new(er) machine.
As for Byte, they routinely sold older machines based on what customers wanted (and could afford). There's nothing at all unusual about this; EB Computers in Fairfield specialises in older Macs as well. Premium dealers like London Drugs and Best Buy and Staples don't do this, but most smaller/independent computer dealers do. It's a very common practice, and while they probably should have let you know that it was an older model at the time you bought it, you still got seven years of service from it; I don't think it owes you anything at this point, you definitely got what you paid for it out of it.
As for buying new: nothing in this world is guaranteed, but particularly with the Apple-made chips Apple is now using, I suspect they plan to stand behind them at least as well as they have previously stood behind the Intel chips. If you buy a new Apple computer and you want the maximum lifespan from it, that's simple: buy the latest model, and buy AppleCare+ to go with it. The AppleCare+ warranty can be extended beyond the three-year mark (though the procedure is a little complicated; see
here for details) as of last year if you're buying the latest model from an Apple-authorised dealer (again, such as Best Buy, Staples, London Drugs, and possibly Costco).