Impeachment should be an apolitical process that seeks to protect the Constitution. It shouldn’t be a way to drum up political support for some idea, an advertising piece for a political campaign, or otherwise a bit of flim-flam.
In general, there should be laws or Constitutional amendments that ensure this but, in their absence, we have to look at the existing body of code.
Maybe there is more but, that I have found in a brief search, the only law that might be applicable to members of Congress would seem to be 18 U.S. Code § 1512 (Witness Tampering), from section b on.
The President could choose to take a fairly wide view of “tampering” where, effectively, any public or politically-minded statement by anyone in Congress is viewed as a threat or element of “influence” towards witnesses to testify in one way or another. Likewise, any release of testimony that would be relevant to an impeachment proceeding, would influence the answers of later witnesses - to avoid contradictions that might cause perjury accusations, to coordinate responses in the name of covering the crime, etc.
None of which would prevent Congress from holding impeachment hearings nor voting to impeach, it would just require them to protect the sanctity of the investigation during the investigatory phase.