On Windows, when Opera is in fullscreen mode and I hit ctrl + t, a new tab is opened and Opera immediately switches to it as I would expect. There's no address field in that new tab in fullscreen mode though to type an address to go to, but I can click on my speeddials etc. Old, Presto-based Opera had an option where if you pressed F2 (in fullscreen mode or not), you'd get a dialog with an address field where you could type an address and press enter. Something like that in current Opera might be nice.
In current Opera, you can do a little hack in fullscreen mode after you hit ctrl + t. You can then hit ctrl + shift + j to open the console, type document.location = "https://example..com/"; and press enter. But, it's probably just easier to F11 out of fullscreen, type the address, press enter and hit F11 again to go back to full screen.
Opera does have ctrl + tab and ctrl + shift + tab to cycle between tabs, which works in fullscreen mode too. That can be useful. If you want an instant no-visual switch, you can use ctrl + pageUp and ctrl + pageDown instead.
Having an option to show the address bar and tab bar when hovering at the top of the page while in fullscreen mode like you said Edge does, might be nice.
https://forums.opera.com/category/15/suggestions-and-feature-requests is where you can post feature requests (one request per post).