Google's site command will show the URL you put into Google for the site command, even if the URL itself has been redirected using a 301 redirect. I believe it has worked like this for years and years. But Google's John Mueller and Danny Sullivan are now defending why Google does this.
The domain thesweethome.com 301 redirects to thewirecutter.com, no one will argue that. But when you do a site command for [site:thesweethome.com] in Google, Google lists thesweethome.com and not thewirecutter.com.
This is intentional and has been how Google does this for years, as far as I can remember.
Here is Danny Sullivan's response on why:
I think that if you site: for a specific domain, we'll show the domain you searched for regardless of the 301 even though we'll recognize the 301 for ranking purposes. @JohnMu might be able to say better.
— Danny Sullivan (@dannysullivan) January 14, 2019
Again:
Again, if you site: search, you're going to get the old domain the reason that @JohnMu explained -- you specifically asked for it. But if you are not, you are going to get the redirected domain just fine. pic.twitter.com/AI4T8wqn3z
— Danny Sullivan (@dannysullivan) January 14, 2019
John Mueller's turn:
We know that the old URL is equivalent to the new one (clicking on the old one goes to the new one), so we may show the current (new) content with the old URL, if you're explicitly asking for the old URL. We're not showing the old content if we've processed the redirect.
— 🍌 John 🍌 (@JohnMu) January 14, 2019
If you do a rebrand and people explicitly search for your old one, I think showing them where to go is a good approach. I realize y'all use site:-queries for website/search diagnostics, but ultimately they're for users.
— 🍌 John 🍌 (@JohnMu) January 14, 2019
So you'd prefer not to be found at all after a rebrand? That feels like a weird approach to rebranding.
— 🍌 John 🍌 (@JohnMu) January 14, 2019
I kind of agree with Google here.
Forum discussion at Twitter.
