But impeachment applies to high crimes and misdemeanors, not to being mentally incompetent and a political liability. What would the impeachment charge be?
Impeachment is a political, and not a criminal, procedure. As you noted, impeachment must involve “high crimes and misdemeanors”. But those crimes are whatever the House of Representatives defines them to be!
So in Biden’s case, the House could define his crime to be “neglectful in his duties”. Or darn near anything else.
Benjamin Franklin even once remarked that a president could be impeached just for being rude.