I found that focusing any input element makes the extension do strange things. The bug can make keyboard-only usage of the entire website impossible. At first, I thought it's a browser bug, so I even asked a question on stackoverflow, only to find out that it's in fact caused by this extension.
The problem doesn't actually seem to have anything to do with passwords at all. You can find a description, including an example, in this codesandbox (if you have no technical understanding, just ignore the code part on the left and focus on the rendered part on the right): https://codesandbox.io/s/input-element-destroys-focus-behaviour-bydvv
Note that the input field does not even have type="password".