You sure are a thirsty boi now aren't you?
"The case of U.S. v. Nixonin which the Supreme Court ruled that the president had to turn over the infamous Oval Office recordings to the special prosecutorwas decided just over three months after the relevant grand jury subpoena had been issued.
That was a criminal investigation, so the analogy is not entirely apt"https://www.lawfareblog.com/what-powers-does-formal-impeachment-inquiry-give-houseThe subpoenas were issued based upon a criminal proceeding.
The quote you gave undermines your argument that "impeachment" and "criminal investigation" is one in the same. "So the analogy is not entirely apt" = criminal investigations aren't impeachment proceedings. The case of "U.S. v. Nixon" wasn't an impeachment, it was a criminal investigation.
Impeachments can be carried out on the basis of criminal proceedings but do not necessarily have to be. They are not themselves criminal proceedings, as the president isn't being charged with a crime through the determination of an impeachment.
The Nixon impeachment was based upon the criminal Watergate incident, so yes, it was a criminal proceeding.
You were wrong. Just admit it.