Jane Sanders assured me that her husband won’t be declaring his candidacy for president Thursday in Vermont when he addresses the first, invitation-only gathering of the Sanders Institute, surrounded by many of the people who powered his 2016 run.

“He’s just a speaker at this,” Jane Sanders said this week. “And, Joe, really, he hasn’t decided yet.”

Nobody believes that. Certainly not anybody who heard Vermont Sen. Bernie Sanders light up the Berkeley Community Theater last month with a 45-minute speech where you could almost hear him revving up the campaign bus. There, before the friendliest of deep-blue audiences, the 77-year-old independent presented himself as someone who could both tear into President Trump and unify the country.

But what happens this weekend in Vermont will be more important to the progressive movement over the long term than what Bernie Sanders inevitably announces in the next few months. The Sanders Institute, built on the momentum of Sanders’ iconic, improbable and influential 2016 run, is aiming for something bigger.

It is trying to make Sanders’ main ideas — Medicare-for-all health care, tuition-free college and a livable minimum wage — part of the political mainstream long after Bernie leaves the stage. And it’s trying to expand the audience for what Jane Sanders calls the “bold ideas” beyond the choir.

Several Californians — including former nurses union boss RoseAnn DeMoro, San Francisco Supervisor Jane Kim, Stockton Mayor Michael Tubbs, health care policy leader Michael Lighty of Oakland and the AIDS Healthcare Foundation’s Michael Weinstein — will play key roles this weekend and beyond in trying to push progressive politics into the mainstream.

Jane Sanders is adamant that the three-day gathering of 250 progressive leaders — dubbed “The Gathering: A Gathering of Minds to Envision the World We Want” — is focused on building an international movement. It is not about fueling Bernie Sanders’ 2020 White House aspirations, she says.

“Bernie has always said this is not about him,” Jane Sanders said. “It is more important that the ideas are resonating. The important thing is to keep moving forward.”

The mainstreaming of progressive ideas took a leap forward during the midterm elections. There was Katie Porter, a Democrat who won a House seat in Orange County on an unabashedly progressive platform, and Democratic Rep. Beto O’Rourke’s near-miss of a Senate campaign in Texas. After seeing the popularity of Sanders’ refusal to accept money from corporate PACs, 170 Democratic candidates for House and Senate followed suit this year.

As Sanders himself said last month in Berkeley, even though his 2016 presidential campaign wasn’t successful, “the ideas we were talking about” that “seemed so radical, so fringy, so extreme ... they are now part of the mainstream conversation.”

Kim knows that firsthand. She has long been an advocate for free college tuition. Momentum soared for her plan to make tuition free at San Francisco City College after Sanders started talking about the idea on the campaign trail.

“Absolutely,” said Kim, who will be giving a presentation at the Gathering on how other cities can replicate City College’s plan. “It was an inspiration.”

However, several Gathering speakers said progressives need to reach more diverse audiences to grow. The Gathering will feature discussions on civil rights and criminal justice; author and Black Lives Matter advocate Shaun King will be among the speakers.

It’s a nod to critics who said Sanders didn’t focus enough in 2016 on how racial and economic issues are intertwined. Sanders himself went in that direction when he said in Berkeley, “We have a criminal justice system that is not only broken but racist.”

“Sen. Sanders was certainly pushed on race during the campaign, and rightly so,” Kim said. “When you’re in the public sphere you’re constantly pushed to be better, and I think this is a response to that.”

Mainstreaming big ideas like Medicare for all will also mean coming up with plausible ways to pay for them. Lighty, a longtime policy expert for the National Nurses United in Oakland until he left the organization in May, will unveil findings Friday on how to pay for a Medicare-for-all health care plan. The new plan, which will detail how to replace the current system with a publicly financed one, is the result of more than two years of research by Robert Pollin, a professor of economics at the University of Massachusetts.

Lighty said he hopes the new plan could surface soon in California, where Gov.-elect Gavin Newsom is more receptive to single-payer than Gov. Jerry Brown was. A single-payer plan — with no funding mechanism attached — cleared the state Senate last year before being shelved in the Assembly.

“Gavin’s leadership is the difference-maker here,” Lighty said. “Absolutely we should do this in California. It’s the type of bold solutions we need to be looking at.”

Joe Garofoli is The San Francisco Chronicle’s senior political writer. Email: jgarofoli@sfchronicle.com Twitter: @joegarofoli