Sorry to hear about your problems with the 2010 27" iMac, I got a used one back in 2015 or so for a pretty good deal and just recently decided to retire it, as it was no longer able to run the tax software that I use. They make a great platform as a media/entertainment center for music, photos, movies, but a lot of current versions of software and the current macOS won't run on it anymore. On the other hand, if you have a similar vintage printer/scanner then those drivers might not be available either, so if you upgrade to a new mac and OS, you might also need to upgrade to a new printer/scanner if you can't find the compatible drivers for it.
Those are the last models where it is actually not totally impossible to open up and access the internal drive bay, and you even have an additional interface that you probably did not know you had in there. I have seen some folks modify that to add an extension cable and mount an additional eSATA port on the bottom of the case to make use of it. I think it was for like a build-to-order fusion drive option so there was another socket for a SATA blade SSD. I replaced my 5400RPM drive with an SSD and the machine ran very quiet, since the drive did not make noise and it ran cooler so the fans barely ever came up to speed either. They also were some of the last models to have a built-in DVD drive, which is handy sometimes, and they supported Target Display mode with the older laptops, if you ever needed to use that feature. But, alas, it was time to upgrade and retire that machine, I understand the attachment to it, they were great machines in their day. Some of those might support up to 32GB, but typically were limited to 16GB, so while that might still be sufficient for most folks, newer models give you more capacity for expanding RAM.
I like to make a bootable clone of my internal hard drive on all my Macs, using Carbon Copy Cloner. Then when the internal fails, I can just reboot the machine on the external backup drive and perform the restore tasks, or get a new drive up and running after replacing one. If you can't boot from a USB drive there might be more problems with the computer than the internal drive. You could try to reset the SMC to see if that helps you boot on a USB drive.
You might consider looking for a good deal on a used Mac from late-2015 or later if you want to be able to run the current version of macOS and don't want to spend money on a new current model.
