I use Edge on all my devices. And on a Samsung Galaxy S10+ it works as it should - address bar is visible and functional. It's just the Surface Duo where I encounter the behavior described in the OP.
This has been going on for several months. I reported it as well, but didn't get any reaction. I find it strange that this problem occurs on Microsoft's own device, but is absent on Samsung devices. I would expect MS Edge to work best on a Microsoft device.
My workaround has been to put bing.com in the favorites and then, each time I want to type a URL, visit Bing via favorites and then type the URL into the search box. Altogether I find it disappointing that this problem has not been fixed yet after multiple months.
I use Bing daily on the Surface Duo and noticed I could browse to sites with the search and knowing how much Microsoft makes changes, I thought they changed how we Edge worked. Glad I found this thread and see I'm not the only one with this issue. My main phone is also a Samsung and Edge works fine on it.