Monterey Updates

Sorry, a late 2013 iMac can be upgraded to Catalina 10.15.7 but no later

See the following from Identify your iMac model - Apple Support

iMac (21.5-inch, Late 2013)

Model Identifier: iMac14,1

Part Number: ME086xx/A, ME087xx/A

Latest compatible operating system: macOS Catalina 10.15.7

No. The latest system your iMac will run is Catalina, 10.15.7. The following list of compatible iMacs is from this Apple document; macOS Monterey is compatible with these computers - Apple Support

iMac

Learn how to identify your iMac.

• • • iMac (24-inch, M1, 2021)
    • iMac (Retina 5K, 27-inch, 2020)
    • iMac (Retina 5K, 27-inch, 2019)
    • iMac (Retina 4K, 21.5-inch, 2019)
    • iMac (Retina 5K, 27-inch, 2017)
    • iMac (Retina 4K, 21.5-inch, 2017)
    • iMac (21.5-inch, 2017)
    • iMac (Retina 5K, 27-inch, Late 2015)
    • iMac (Retina 4K, 21.5-inch, Late 2015)
    • iMac (21.5-inch, Late 2015)