I am very much a fan of Disk Warrior. It has saved my bacon on more than one occasion. Of course, you won't know if it can fix it until you try. You can use DW with a Time Machine backup but, in my experience, it takes a long time. For comparison purposes only, my TM drive has a capacity of 500 GB and DW takes 20-30 minutes to go through its routine. Rebuilding the directory on my main drive (while booted from a clone) takes 5 minutes or less. If you have a lot of directory errors, it can take much longer.
Assuming that DW can fix this, your next TM backup should not have this error so, unless you need previous backups, it shouldn't matter.
Before spending the money, you might want to post the DU log of the directory repair. Someone may be able to give you a better answer.
Jon
macOS 11.7.10, iMac Retina 5K 27-inch, late 2014, 3.5 GHz Intel Core i5, 1 TB fusion drive, 16 GB RAM, Epson SureColor P600, Photoshop CC, Lightroom CC, MS Office 365
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