High crimes and misdemeanors is a legal term of art. Impeachment and conviction are political acts, so are not bound to find an offense against a statute. Being a political act, the babsis for impeachment has to pass the smell test with the public. Generally this means making an allegation that at least looks like a violation of some statutory crime.
There are remedies and powers limitations to the Congress. All they can do is remove a person from office and ban them from future office. If there is a crime, that has to be taken up by the executive in an eforcement action, and tried in an Article III court.