“Progressive government by definition must be functional,” the governor said, returning to a common theme and citing his father, the former governor, Mario M. Cuomo.

The governor’s address kicks off the start of the year’s legislative session, and comes on the heels of a historic year in Albany, where lawmakers passed major new laws on rent, climate change and congestion pricing, among other issues.

Last year was also a period of transition for Mr. Cuomo: For the first eight years in office, Mr. Cuomo worked with a Republican State Senate, which often backed his pleas for fiscal austerity and batted back progressive reforms. That changed in the 2018 midterm elections, when Democrats took control of the Senate with the help of a number of young, liberal candidates who repeatedly challenged Mr. Cuomo, sometimes leading to heated conflicts.

That rift has already surfaced this year, as the governor and other Democrats grapple with the political fallout from a new law that sharply reduced the use of cash bail. The law went into effect on New Year’s Day, and since then, concerns over a spate of anti-Semitic incidents and other recent alleged crimes committed by those released have led to calls for changes in the law, including by Mr. Cuomo himself.

Mr. Cuomo made no mention of the bail reform on Wednesday during his speech, which included quotations from George Washington, Henry David Thoreau and the singer-songwriter Leonard Cohen, and an extended nautical theme, with mentions of rocky shores, rough seas, and a “political and social superstorm” of anger and divisive rhetoric.

Considering the state’s financial straits, Mr. Cuomo leaned heavily on proposals that would need little or no state funding, like banning gun ownership for people who have committed certain misdemeanor crimes in other states, banning foam food containers and outlawing synthetic opioids similar to fentanyl.