S.m.a.r.t. Error

That iMac can't run any version of macOS later than High Sierra. Replacing the internal hard drive would involve fairly involved surgery (probably not worth paying a repair shop to do, for such an old machine).

The machine doesn't have USB 3.0 (or better) ports – just USB 2.0 ones. So most external drives on the market today would run at USB 2.0 speeds – making them S-L-O-W startup disks.

If you do want to hold onto it a bit longer, one option might be to get an external (Firewire 800 + USB 3.0) drive, make that your startup drive, and stop using the internal drive for anything. You would use Firewire 800 now – and USB 3.0 when the time came that you wanted to use the drive with a new machine.

OWC is the only vendor that I know about who still sells such drives and enclosures.

https://eshop.macsales.com/shop/firewire/1394/USB/EliteAL/eSATA_FW800_FW400_USB

https://eshop.macsales.com/shop/firewire/on-the-go

I'm using one of the "On The Go" enclosures, with a separately-purchased SATA SSD, on a Late 2009 iMac. The Firewire 800 interface bottlenecks the drive enough that it does not deliver the blistering speed that one usually associates with a SSD. However, performance is decent. I normally eject the internal hard drive, which causes it to spin down, the result being that there is no drive noise from either drive – only noise from the iMac's fans.

The hard drive is failing.

I would say replace the hard drive, but on a 2011 iMac, it’s probably not worth it. That Mac is not capable of running any supported version of macOS.

It probably goes without saying – but if you have anything on that failing drive that you want to preserve, and that has not been backed up yet, the time to back it up is now.