The Web browser widget does not appear to accept keyboard input until clicked. Even when opening a web page that has a text box that is selected by default (such as in the test project provided) and "Set Keyboard Focus" has been called for the web browser widget
Result: The text box on the web page appears to have focus but does not until it is clicked
Expected: After providing the web browser widget with keyboard focus, it would accept input from the keyboard
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-53165 in the post.