pablitoviejo wrote:
Can I continue to use my late 2013 iMac, or is it outdated?
It is very outdated, but as long as it does what you need it to do, you can continue to use it.
I have a lovely iMac late 2013 iOS 10.15.7.
Am I to accept that Apple wants to make it outdated so I have to buy a new one?
Regardless of Apple's motivations, and regardless of whether you want to "accept" it, that old iMac is outdated. It might still be useful – I used a 27" Late 2009 iMac long, long after it became outdated. But technology moves on. (If it didn't, we would be stuck with machines with the capabilities of the TRS-80 or the Apple II.)
That Mac originally shipped with Mac OS X 10.8.4 (Mountain Lion). macOS 10.15.7 (Catalina) is the end of the line, which means that Apple provided you with seven free major macOS upgrades. Catalina is now six major versions behind Tahoe (the current version of macOS), at the point where even some developers with a history of offering software for old versions of macOS may be thinking of abandoning it.
Apple switched from Intel processors to Apple Silicon ones starting in 2021. Their product lineup now contains no Intel-based models. Only four Intel-based models can run macOS 26 (Tahoe), and Apple has announced that the next major version of macOS will not support any Intel-based Macs.
There have been a few improvements in speed in the course of 10+ years. For instance, here is how 24" M4 Macs compare to 21.5" Late 2013 iMacs in single-core CPU benchmarks.

The USB4 / Thunderbolt 4 ports on the M4 iMac are also much faster (for connecting high-end gear), and much more useful for modern gear, than the Thunderbolt 1 ports on the Late 2013 iMac. (Those are now useful mainly as Mini DisplayPorts.)
Can I continue to make use of this still wonderful machine which has one terabyte of solid state memory installed.?
Yes, if you have – or can still get – the applications that you need.
Vendors like Microsoft and Adobe, who have a policy of supporting the "most recent three", abandoned Catalina a long time ago. Catalina is also ineligible to receive current versions of Safari, Pages, Numbers, and Keynote.
Current versions of Firefox, LibreOffice, and the Affinity Suite (free with registration, as long as you don't want the AI features) will run on Catalina. Current versions of other major third-party browsers now require Monterey – and thus are incompatible with your machine.