The macintosh runs high sierra fyi, It is pretty much non functional other than when it starts into macos utilities.
Earlier Mac models
That 2011 iMac is fourteen (!) years old. It has lived a long and productive life and it wants to retire.
You should let it.
Recycle responsibly.
What to do before you sell, give away, trade in, or recycle your Mac - Apple Support
A 2011 iMac shipped with gray system install restore disks. Could one of those be in the optical drive?
As a test, try booting while holding the OPTION key to invoke the Startup Manager. That should show if your regular drive is available for booting. Select that drive if available.
If it does not show in Startup Manager, then the drive is damaged or disconnected.
Ways to start up your Mac - Apple Support
Is your internal drive backed up?
One likely reason would be is that the main startup drive is damaged. Having nowhere else to boot to, the Mac goes to the Recovery startup.
Why does my macintosh 21.5 inch from 2011 keep starting up into macos utilities?
