OP wrote:
"Mac os says it cannot repair the internal drive and to backup soon."
Two ways forward that I can see:
1st way...
Drive has a hardware failure. Since you have revived the iMac with an "external booter", I'd just leave the internal drive "dead, but in place". Just ignore it.
Goodgawd No. USB 2 is much slower than replacing the HDD. Thunderbolt is as fast but a dock costs $179 plus the drive and that doesn't change that 9 year old NV RAM battery.
Labor to do both should run $75 if the OP doesn't want to do it.
Drive has software corruption. In that case, I'd erase it with Disk Utility then run the "first aid" function on it. IF disk utility gives "a good report", I'd repeat the first aid function five times in a row. IF I got a good report every time, I'd recommend that the drive be used, but that it be backed up frequently.
That's not going to happen.
I have replaced hundreds of these drives (2009–2012 iMac). Disk Utility will pop up something in red. Repeat and the error will likely change — that's good. If you get the same error three times in a row, give it up.
If the error goes away and you get green (I've run DU up to 50 times to get that), get your data off that drive ASAP. This will last anywhere from 15 minutes till... I saw one last a few more days before doing it all over again. One out of hundreds.
I've remapped these drives to write around the bad sectors but it never worked, not once. You can spend a lot of time down this rabbit hole but I've already done it for you.
The only thing you can accomplish is to get the data off the drive. It cannot be revived. The only surprise is that it lasted this long. They're usually having these problems within 5 years.