Imac 2017 27' Catalina installation error, storage error (-69716), what to do, ? on desktop Mac

That's a pretty serious error for which the only solution appears to be reinstalling macOS. First, shut down the computer by holding down the Power button until the computer shuts down. Second, you need to reinstall macOS. The easiest way is to use a bootable USB flash drive installer if you have one. If not, then do the following, which assumes the Recovery Mode is functional.

Boot Using OPTION key and USB Flash Drive Installer

1. Restart the computer.
2. Immediately, at or before the chime press and hold down the "OPTION" key.
3. Release the key when the Boot Manager screen appears.
4. Select the disk icon for the USB flash drive. It should appear with a name like, "Install macOS [version]".
5. Click on the arrow button under the drive icon.

Install El Capitan or Later from Scratch

If possible, back up your files.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the target drive (out-dented entry w/type and size info) from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the partition scheme to GUID.
6. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
7. Click on the Apply button, then wait for the Done button to activate and click on it.
8. Quit Disk Utility and return to the Utility Menu.
9. Select Install OS X and click on the Continue button.

If the Recovery Drive is no longer functioning, then you need to use Internet Recovery. You will need a fast Internet connection, Wi-Fi or Ethernet. The latter would be preferable.

Internet/Network Recovery of El Capitan or Later on a Clean Disk

     If possible, back up your files before proceeding.

1. Restart the computer. Immediately, at or before the chime, hold down the (Command-Option-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the target drive (out-dented entry w/type and size) from the side list.
5. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs, only if installing Mojave or Catalina ) or Mac OS Extended, (Journaled.)
8. Provide a volume name, usually "Macintosh HD."
9. Click on the Apply button, then click on the Done button when it activates.
10. Quit Disk Utility and return to the Utility Menu.
11. Select Install OS X and click on the Continue button.