macOS Catalina
Will Catalina continue to receive security updates? If yes, any idea for how long? Thanks!
(iMac late 2013)
If history is any lesson, likely for a few more years however Apple does not normally announce that type of information. Please remember as long as your 2013 suits your needs and works okay then it is likely just fine.
That being said though, please also remember it is now 10 years old and you should be considering and saving for its replacement.