On what basis is congress subpoena'ing University of Columbia's
president (other presidents of private universities)?
Congress has very broad subpoena power to investigate situations that take place in the real world to determine if it is possible, feasible, or desirable to make new laws related to almost anything.
It can also use its subpoena powers to determine if existing laws have been violated, or if existing laws have been enforced inappropriately.
While the Congressional subpoena power isn't absolute, in terms of permissible subject-matters, it comes close.
The issue is that Congress needs to have some idea about what is going on outside the Capitol to do its job, and doesn't want to be beholden strictly to private sector news reports or data gathered by the Executive Branch.
For example, maybe the National Enquirer says that protests on campuses over the Israeli-Hamas war are real, but are actually being conducted by disguised lizard people and Yetis; the New York Times may say that those protests are real and are being conducted by regular human college students in response to news reports on that situation; and some conservative bloggers may deny that there protests are happening at all claiming that they are just a big Deep Fake produced by a mainstream media conspiracy. Suppose further that members of Congress don't agree on which version of the story is correct. Congress, rather than relying on secondary sources to determine what is really happening, may want to subpoena some witnesses with first hand knowledge to tell them, under oath, what is really happening.
There are all sorts of reasons that Congress would have legitimate interest in the affairs of private higher educational institutions, not least of which is the fact that Congress provides a substantial part of the funding for these institutions.
There are significant constitutional limitations on what kind of legislation Congress can pass. But until somebody investigates the facts, Congress can't know, when there is a dispute regarding the relevant facts, if existing laws are working just fine, or if existing laws are giving rise to something that some member of Congress thinks is a problem and should be changed in a way that Congress has the legal authority to address. By its very nature, Congress routinely needs information about matters for which existing data collection is inadequate to provide guidance to it in legislating, because no existing laws call for that kind of data collection.