What are my options to upgrade or trade-in an iMac 21.5-inch, Mid 2011?

Apple will recycle a 2011 iMac at no charge however it has no commercial value so you will not get a trade-in credit. You can learn about Apple's recycle program by clicking Apple Recycling Programs.

If you want to get money for it, your best option is to sell it privately. If you take it apart and sell individual components (display, main logic board, power supply, GPU) you will likely get more money.

Best of luck!

The 2011 iMac is too old to be of any value as a trade-in.

to check, go to > Apple Trade In - Apple

So basically if you use their Trade-in option, they will just recycle it.

You can also repurpose it for another family member or maybe get a couple of hundred dollars selling it on your own. But keep in mind that it needs to be properly prepaired before repurposing, giving away, donating, recycling or selling.

to do that, see > What to do before you sell, give away, or trade in your Mac - Apple Support

macOS High Sierra 10.13.6. Trade-in options - none. However, any Apple Store will accept it for recycling at no cost.