Can you give a few examples of common programs that use this? I've never heard of it and a quick search doesn't find me anything that uses this.

Also I wonder if this would be better as a shortcut defined as a setting rather than hardcoded.

Not exact behavior but in the browser, terminal and gtk applications, ctrl-u clears the text from the cursor/caret to the beginning of the line, at least on linux.

Is it common as a shortcut on the web? I've never heard of it, and opening the page source is built into the browser.

Regardless I don't think anyone really cares to open the page source on the search page so it's fine being hardcoded imo.

I have no problems with this. Just fix tests. _onClear doesn't expect a keyboard event. You should be able to change the type on a generic Event type instead.