After performing redirect to a new domain
I tried to inspect the old domain URL from its webmaster and I got this info
URL is not on Google This page is not in the index, but not because of an error. See the details below to learn why it wasn't indexed. Learn more
If yes, so why I am still losing my rank in google search?
Also, I would like to know What's the difference between the Referring Page and User-declared canonical?
Google doesn't index redirecting pages and that is perfectly normal. Google is saying that the new domain is the preferred equivalent URL and that it isn't going to index the old domain because of the redirect.
There is nothing in what you posted that would indicate why your rankings are dropping. Google usually preserves rankings when changing domain name using 301 redirects. Especially if you used the Google Search Console change of address tool. For further help with ranking drops see How to diagnose a search engine ranking drop?
The user-declared canonical is what you (the user) have told Google (declared) to be the preferred URL (canonical). In this case you used a redirect to tell Google about the preferred URL.
Google has the ability to choose a different canonical than the one that you indicate. If Google chooses a different URL, it would tell you in the "Google-selected canonical" field.
The referring page is where Google found a link to your URL. In this case Google says there is none. I wouldn't necessarily believe that though. Google doesn't do a very accurate job of reporting referring URLs in my experience.
