Why is my external HDD failing to mount on my MacBook?
Why exactly did this happen on a disk that was working perfectly fine, driving down the same road the day before?

For the exact same reason your car breaks down on the road when it was working perfectly the day before.  In other words C'est la vie.
Is it your drive or the enclosure?
Now, as to your situation, you've presumed that the drive went bad without ruling out the other factor - the enclosure itself. The USB port would be the third factor, but you automatically ruled that out by going to a different computer.
There's a very similar question to yours already posted:  External Hard Drive no longer working.  That one involves an enclosure and an SSD, not an HDD like yours, but the principles are the same.
Recovering your data
It's a bit confusing as to what's exactly on the external drive - data or backups.  If it's backups, there's really no need to expend the time and money to recover something.  Get that external SSD and just continue making backups like you normally have.
If it's data - you need to determine what that data is worth to do.  For data recovery, I've used DiskDrill; it's absolutely free to scan and see if your files are recoverable and if they are the software is (IMO) reasonably priced at $90USD.  If your data needs to be recovered, it's a cheap price to pay to get it back - it's also a good reminder to back up your data wherever it exists; - on your boot drive and your external drives!