If this is a sudden change after a very long time of working correctly, and it's always the second two on any page, I would suspect it's the eBay generation software rather than the printer itself.
The only suggestion I'd have is to see if there are updated device drivers for that printer and to give installing them a try. If that doesn't work I'd nag eBay (and, yes, as a long time eBay-er I realize that has an almost zero chance of success).
While I agree that the second font isn't as easily human readable, it seems human readable and the bar codes and QR codes still seem fine, which is what the shipper will be scanning to route the package, anyway.
I definitely know what you mean about peel and stick labels. I have no idea why your Dell Printer would smear them unless the label sheets themselves were designed specifically for laser printers. I can print all sorts of address labels on my Canon inkjet printer without issue, and that's been the case on many models of Canon for several decades now.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
. . . the presumption of innocence, while essential in the legal realm, does not mean the elimination of common sense outside it. The willing suspension of disbelief has its limits, or should.
~ Ruth Marcus, November 10, 2017, in Washington Post article, Bannon is right: It’s no coincidence The Post broke the Moore story