If the problem occurs while listing, then my general laundry list of things to try may not be much help, as you are pretty much stuck following the link you are already using unless you can switch to another listing tool, or switch between app, mobile browser, classic site or desktop site versions. One possible exception, though, once you get caught in a sign-in loop, is to try signing in using a social media account rather than your username and password. That may bypass whatever dependency is causing the loop.
There are many possible things that can contribute to a difficulty signing in. Hard to know which one, if any, is tied to the latest issue, so here is a laundry list of general things:
If you are using an old bookmark, try going directly to the main ebay.com page and sign in there instead.
Try another browser or the eBay app. Preferably the latest version of a popular browser, using default settings and no add-ons. Or a private or incognito browser window.
If you are using popup blockers, script blockers or tracking protection, try disabling those on the sign-in or verification page.
If you are using a VPN, try disabling that.
If you are using privacy software like Disconnect or Ghostery, try disabling that.
You may be able to avoid the loop by signing in using a social media account instead of using your username and password, if you have previously linked a social media account to your eBay account.
