How do I update iMac to iOS 13 or later

You don't. For your Late 2015 iMac, macOS 12 (Monterey) is the end of the line.

Note that, depending on what you are trying to do, there may be alternatives.

Monterey is not one of the "most recent three" – currently Sonoma and later, soon to be Sequoia and later – but it is enough to run current versions of

• Firefox and most other third-party Web browsers
• LibreOffice
• The GNU Image Manipulation Program (GIMP)
• The parts of Affinity Studio that are "free with registration"

Hi,

You could upgrade farther than Monterey, though we shouldn't discuss about it here.