Yes, your first screenshot is what we call (and you should call) the Web Vault. The second screenshot is what we call (and you should call) the Browser Extension (specifically, you have opened the “Vault View” in the Browser Extension, and then filtered your vault items by the “Login” type).
[And FYI, I have again replaced your screenshots by new versions, in which I removed your exposed email addresses…]
Starting with your second screen shot (“Vault View” in the Browser Extension, filtered by “Login” type), please click on any of the items that have a globe icon, which should show you the details view. Just below the obscured password field, look for one or more fields that are labeled “Website”, then click the copy (❐) icon in the right margin (as shown at call-outs 1 and 2 in the screen shot below) and paste into your response.
It would be especially interesting to see your results for a site where you were able to get the success message “Item filled and URI saved” when using the “Auto-fill and Save” function. In any such cases, I would expect there to be two “Website” values saved in the item, similar to what is shown in the screenshot above; please copy both values (one at a time) and paste each into your response.
In addition, please report the value copied from the “Website” field for other login items that have a globe icon, for which you have not tried (or not succeeded with) “Auto-fill and Save”.