If you are able to list with one account but not another, something about the first account must be different or requiring a different verification process. I do not see any listings on your current account which was created today, so I cannot check to see any particulars. Anything odd about your location or network? Did you change countries or country settings, or use a VPN?
General suggestions when dealing with verification issues:
Disabling ad blockers, pop-up blockers, script blockers or other privacy tools on the sign-in or verification page can help; many of those have settings that can interfere with verification. You may be able to turn them back on once you have signed in and updated your eBay cookies.
If you are using Firefox, try disabling Enhanced Tracking Protection on eBay using the shield icon to the left of the page address.
If you are able to sign in and go through verification using a private or incognito browser window, that might indicate a problem with a corrupt or blocked cookie. Try erasing just your eBay cookies manually in that case.
If you are routinely clearing all your cookies, you will likely have to go through verification again each time you sign in.
Or try a different browser -- preferably the latest version of a popular browser that you do not normally use and one that has no add-ons or extensions installed.
Or try a different device altogether; it may be that you can complete verification using a mobile browser or the eBay app.
More things to try can be found here, though it primarily deals with sign-in issues:
https://community.ebay.com/t5/Member-To-Member-Support/Whatsup-with-3-levels-of-authentication-just-...
Otherwise it might be useful to contact eBay and see what verification is needed and if there is an alternate path to completing it.
