I’ve heard this idea expressed before. But I know of no article of the Constitution or federal law that offers criminal immunity to the President of the United States. Maybe you could enlighten me on this little detail.
The impeachment process is basically his trial
The house first hears the articles, the witnesses and the evidence
If he is found guilty (like Clinton was ) then the Senate determines his consequences which can be removal. If you recall Since Clinton committed sexual crimes before he was in office and the statute of limitation would have run out the court ruled he could sued and would have to give written statements or appear before the parties involved. That’s iirc led him to perjury and loosing his law license But it was handled as a civil matter not criminal. Criminal they would have had to remove WJC from office before they could charge him with rape. Or murder or theft or .....