External hard drive I use for Time Machine corrupted, won't mount
You’ve got the classic dilemma.
How much would you pay to get your data back? If you allow fsck to “repair” the drive, it might repair the volume structure by removing references to legitimate files. But to learn that, you have to pay for data recovery.
You could say yes and let it repair - it’s often a small error and quickly resolved. But, with Time Machine - you could also wait weeks if there are hundreds of backup intervals of hundreds of thousands of files and Disk Utility chooses to check each and every one.
For sure - go get a new external and set up a new backup set. Or skip the problem entirely and just erase this disk and see if it’s fine with the next backup.
I’d make an estimate of your value of time / the data / getting a new drive. Good luck with your decision. There’s no “easy” answer since the trade offs are uncertain.
Here’s some relevant posts covering how many days it takes to copy files off a working drive...

Clone Time Machine volume
Repair Time Machine sparsebundle that will no longer mount
Is it unusual for &quot;Verify Disk&quot; on Disk Utilities to take so long on a Time Machine drive?