Governor Gavin Newsom has been a leader in California for over two decades, widely viewed as a Democratic presidential candidate in 2028 and, as of late, clashing hard with Donald Trump.

In interviews, Mr. Pritzker, Mr. Polis and Julia Spiegel, a former top legal adviser to Gov. Gavin Newsom of California who will serve as the group’s top staff member, did not say how many ...