SACRAMENTO — The budget proposal that Gov. Gavin Newsom introduced in January gave California’s new leader his first major opportunity to stake out how he would accomplish the ambitious agenda he touted on the campaign trail.

Many of those plans overlapped with the priorities of the Legislature, and they are reflected in the final $215 billion budget deal reached over the weekend. Lawmakers passed the budget Thursday, sending it to Newsom for his signature. The Senate vote was 29-11, and the Assembly approved it 60-15.

But several key Newsom initiatives were rejected or still await action in budget follow-up bills that the Legislature will consider in coming weeks. Those differences underline challenges the governor will face to achieve signature campaign promises such as creating a universal health care system and building 3.5 million homes by 2025.

Health care: On his first day in office, Newsom announced a sweeping plan to reduce the cost of health care in California and increase access. Two significant proposals that he included made it into the budget:

• California will become the first state to expand eligibility for its health program for the poor to undocumented young adults ages 19 to 25. Those 18 and younger were already eligible for the program, Medi-Cal. The expansion will cost $98 million next year. Newsom rejected calls from Senate Democrats to open the program to undocumented seniors as well, which would have cost another $63 million.

• The state will require residents to carry health insurance, replacing the individual mandate that congressional Republicans and President Trump eliminated in the 2017 federal tax overhaul. Adults in California who do not buy insurance will have to pay an annual penalty on their state taxes of $695 or 2.5% of their household income, whichever is greater. Revenue from the penalty will be used to increase insurance subsidies for individuals and families making up to six times the federal poverty level. The budget also sets aside an additional $450 million over three years to reduce insurance costs further for middle-income people.

After a push by lawmakers, the state will seek to renew its tax on health insurance providers, which brings more than a billion dollars per year into the general fund and draws matching federal dollars for Medi-Cal. The current tax, which the Legislature passed in 2016, expires at the end of the month. Newsom left the proposal out of his budget plan, arguing that the Trump administration would deny the tax, which requires federal approval.

Reflecting the political tensions over adopting a government-run universal health care system, the Assembly has resisted Newsom’s bid to remake a commission that is studying how to change health care in California. The commission was established last year after the Assembly shelved a high-profile bill to develop a single-payer system for the state. Newsom, who campaigned on single-payer health care, wanted to refocus the commission on evaluating options for transitioning to the public model. The issue was deferred from the budget.

Housing: Seeking to spur residential construction and get more homeless people off the streets, Newsom proposed a multibillion-dollar housing and homelessness package.

Most of that money made it into the budget, including $250 million to help local governments plan to reach their state-mandated housing goals; $500 million for infrastructure projects, such as sewer hookups and sidewalks, that support new affordable housing developments; and $1 billion to expand tax credits and loans for building low- and mixed-income housing. The budget also includes $650 million for cities and counties to combat homelessness, and $120 million for programs that offer supportive housing and other coordinated services for homeless people.

But lawmakers are likely to reject Newsom’s bid to withhold transportation funding from communities that do not hit their housing targets. That policy would have to be adopted through a follow-up bill but is deeply unpopular.

Education: The budget takes the first step toward Newsom’s campaign goal of offering universal preschool by adding 10,000 state-funded slots for 4-year-olds from low-income families. It also increases funding for subsidized child care for low-income families with money from the sales tax on marijuana. The state will spend $300 million, half of what Newsom sought, to help school districts build out their facilities so they can offer full-day kindergarten.

Newsom took aim at charter school enrollment with a proposal to ban the schools from requesting students’ academic records before they are admitted and encouraging students with poor grades or learning disabilities to transfer elsewhere. Teachers unions, a strong ally of Newsom’s, dislike charter schools because most do not employ unionized instructors and they compete with school districts for funding. The language is included in a follow-up bill on education spending that is pending in the Legislature.

Community college students will get a second year of free tuition, as Newsom promised on the campaign trail, while the budget funds thousands of additional spots for state residents in the University of California and California State University systems. The state will create two scholarship programs that Newsom proposed: extra financial aid for parents attending college, and state-seeded college savings accounts for children from low-income families.

Clean water: Newsom revived a proposal to impose a fee on water users and polluters that would help communities without access to safe and affordable drinking water, a problem that affects more than a million Californians. The idea fell short in previous years and lawmakers rejected it again, fearing retribution from voters. Instead, the state will divert up to $130 million annually from its cap-and-trade auctions — money meant to support programs that reduce greenhouse gas emissions — to a clean water fund.

911 system: Seeking to update its emergency communications, the state would restructure how the system is funded: A surcharge on landlines would be replaced by a monthly tax on any device capable of dialing 911, including cell phones. The Department of Finance estimates the fee would start at 34 cents per month per device. The Legislature rebuffed the proposal when former Gov. Jerry Brown tried to do it last year, but Newsom brought it back in his budget plan. It must be approved by a two-thirds vote in a follow-up bill this month.

Earned income tax credit: Newsom has thus far been unable to get the Legislature on board with his plan to realign some sections of California’s tax code with the 2017 federal overhaul, which would raise about a billion dollars to expand the state’s tax credit for the working poor. As with the clean-water fee, some lawmakers fear the political fallout of raising taxes. Newsom agreed in the budget deal to keep negotiating over the plan, which the Legislature could approve by a two-thirds vote in a follow-up bill.

Paid family leave: Expanding paid parental leave — from six weeks for each parent of a newborn or newly adopted child to six months per baby — was a centerpiece of Newsom’s early agenda. The budget gets the state part of the way there by giving each parent, or a close family member, two additional weeks to bond with an infant, bringing the total to four months per baby. The expansion also covers leave to care for a seriously ill family member.

To address concerns that poor Californians can’t take advantage of the program because it pays only some of their salary during time off, lawmakers raised the wage replacement rate to 90% for low-income workers.

Government: Newsom got his Office of Digital Innovation, to redesign government services, and hundreds of millions of dollars he requested to reduce wait times and address other workload issues at the Department of Motor Vehicles. The budget also includes a redesigned substance-abuse treatment program that Newsom proposed for California prisons, where drug overdoses are climbing. Lawmakers largely went along with the governor’s $15 billion plan to pay off the state’s budget debts, pay down some of its unfunded retirement benefits and build up reserves, such as the rainy-day fund, in anticipation of an inevitable economic downturn.

Alexei Koseff is a San Francisco Chronicle staff writer. Email: alexei.koseff@sfchronicle.com Twitter: @akoseff