What are you talking about? Embedded browsers use the system webview, provided by Chrome, Firefox, or whatever is configured.

They might hide the URL, so I can't see where the link led me. Or they might disable the usual browser menu, preventing me from bookmarking a page. Or they might have the "close tab" interaction be in a completely different location, breaking any muscle memory.

If I'm following an HTTP(S) link, it means that I want to view it in a browser. I don't want to have some in-app view that can only return me to gmail, or to discord, or to google handouts, just because that happened to be where I clicked the link from. I don't care in the slightest whether the rendering engine is the same as the default browser. I care whether the user interactions are the same.

Yes but how would you even know as a user. Or how would you know that you are on the real google page.

On iOS, yes, since Apple's rules forbid alternate browser engines. On Android, it's not unknown for apps to embed an alternate browser engine in it's entirely.