The house does not impeach, they recommend impeachment, The Senate is tasked with accepting the issue, forming the rules of a trial, and conducting the trial.
It’s going nowhere and is nothing but a media game. If the Senate Pubs actually take this up they can kiss their future careers as representatives goodbye.
Bank on it...
The House does impeach. The Senate then holds a trial at the end of which it votes on whether to convict, and thereby remove from office, the impeached federal official. It's like a grand jury indicting and later the trial jury deciding whether to find the defendant guilty.