I have same problem on win10. Just updated from 72.0.3815.186 to 72.0.3815.207 which didn't help.
Searchbox is not working when opening new speed dial, but it does on existing tab.
When opening new tab and entering some search term, nothing happens.
Workaround is after opening new tab, pressing tab (on keyboard), then shift tab so that focus goes off the search box and goes back. that ''fixes it''. You have to do it on empty searchbox, if you do it when something is already typed in, it will try to open page like http://opera%20searchbox%20not%20working/
Another thing that i noticed, when opening new speed dial tab, while opera is loading that new speed tab (there is x sign left of searcbox - stop loading tab icon), searchbox works, but as soon speed dial tab is loaded it stops working (x icon changes to round arrow - refresh icon).
Also, searchbox works fine when I'm not connected to internet.
At last, not sure if its connected, but I noticed that if I close Opera, it doesn closes completely. Opera window gets closed, but it's still open in task manager. So, if I want to reopen Opera, I have to close processes which is extremely annoying as much as searcbox problem.
This is some wierd bug
If it doesnt get solved by the end of the next week, im switching browsers.