The New York Times dug into financial records of a new group lobbying in support of Governor Kathy Hochul’s proposed $33 billion budget. The group is called American Opportunity. It’s biggest funder is billionaire Michael Bloomberg. Its biggest goals: no new taxes on the rich and more charter schools.

The slick campaign-style ads have been running on repeat during telecasts of “Jeopardy!” and March Madness basketball. They trumpet, at great expense, the agenda of New York’s governor, Kathy Hochul. And at the end of each, a tiny message says they are paid for by a vanilla-sounding group, American Opportunity.

But beneath a maze of shell groups and indirection, the real source of most of the funding for the mysterious new multimillion-dollar campaign to shape the state’s gargantuan budget is a familiar billionaire who once ran New York City and had all but disappeared from state politics: Michael R. Bloomberg.

The emerging alliance between Mr. Bloomberg, a business leader and three-term mayor, and Ms. Hochul, a Buffalo Democrat still struggling to forge a connection with New York voters, could be as significant as it is unforeseen. Though he has become one of the Democrats’ most prolific donors nationally, Mr. Bloomberg did not open his wallet for Ms. Hochul’s 2022 campaign, and sat out some of the state’s most pressing recent policy disputes.

Now, he has given $5 million in seed money to help fund a blitz of television advertising, social media influence campaigns and rounds of mailers targeting individual lawmakers as they grapple with Ms. Hochul over the shape of the budget, according to two people briefed on his giving. Two more people, who also insisted on anonymity, confirmed the gift but not the amount.