My iMac is stuck in recovery mode and I can't get back to my desktop

Please restart the computer in Safe Mode per the directions in the  How to use safe mode on your Mac - Apple Support link.

Note: If you are using a wireless keyboard please either plug it in using the supplied Lightning cable that shipped with it. If you are using a legacy keyboard or a third-party keyboard that does not have re-charging abilities, please use any USB keyboard. Also note that a Safe Mode restart may require you to hold down the shift key for up to 5 minutes before the computer starts in Safe Mode. You will know it is in Safe Mode when you see “Safe Mode” in the upper right of the display.

Next, please restart normally and please retest.

Your footer here shows an iMac Pro, and that’s not available as a 2011 model.

If Safe Mode gets you nowhere… Build yourself a hardware test disk, and boot that and see what the hardware test reports.

The following has links to downloads available from Apple for various iMac models:

https://github.com/upekkha/AppleHardwareTest

Given the vintage and the report, quite possibly a failed hard disk.

It’s possible to boot and use external storage, but the external I/O on the iMac 21.5” 2011 is pretty slow. The other iMac models from 2011 have Thunderbolt, which is decently fast for the era but will require purchasing a Thunderbolt external storage device and those can be somewhat more expensive. USB 2.0 is, well, slow.

Hopefully you have a complete and current backup.

If you do not have current backups, STOP ACCESSING THIS DISK RIGHT NOW—and decide if you want to pay for data recovery. If you do, messing about more with a failed hard disk—whether Safe Mode, or diagnostics, or attempts to reload, whatever—can potentially reduce what data can be recovered, as hard disk failures can tend to be progressive. If you don’t want to pay for recovery and have no backups, you can try getting a backup from Recovery, or using Target Disk Mode. Do that backup first.