President Biden and his aides came into office with deep experience in trans-Atlantic affairs. But over four years, they focused too on the Pacific, where China strains to be the dominant player. Their main effort: building up alliances to counter China.

President-elect Donald J. Trump has already signaled a different approach to China. He invited Xi Jinping, China’s leader, to his inauguration on Monday. The two spoke by phone on Friday, and Mr. Xi is sending China’s vice president, Han Zheng, to the ceremony, a break from China’s tradition of having its ambassador in Washington attend.

The Biden administration’s final activities aimed at China stand in contrast to that. Mr. Biden held a call last Sunday with the leaders of Japan and the Philippines to firm up a new three-way security arrangement he helped build. Secretary of State Antony J. Blinken visited South Korea and Japan this month on his final official trip.

In the telling of Mr. Biden and his aides, they are handing Mr. Trump a sharpened competitive edge on China, the greatest rival to the United States.

Of all of Mr. Biden’s foreign policies, his approach to China could ultimately be seen by historians as existing in a continuum. His administration built its own structure on a foundation of competition laid by Mr. Trump’s team and is now turning it over.

It is unclear what Mr. Trump will do with that. He admires the autocratic Mr. Xi, and sees China mainly through the lens of economic negotiations. Mr. Trump’s billionaire advisers, including Elon Musk, want to maintain and perhaps expand business dealings with China.

But his top picks for foreign policy aides are more aligned with Mr. Biden: They assert that the United States must constrain China across many dimensions, and using the entire range of security and economic tools.

One early test will be whether Mr. Trump enforces a ban of TikTok, the Chinese social media app popular with young Americans.

Mr. Biden signed bipartisan legislation last year to ban TikTok based on national security concerns unless its parent company, ByteDance, sold it to investors not tied to a “foreign adversary.” ByteDance still owns TikTok, and the White House announced on Friday that it would be up to Mr. Trump to enact the ban. Mr. Trump said Saturday that he would likely give TikTok a 90-day reprieve from the ban, and the company’s chief executive plans to attend his inauguration.

Mr. Trump’s signature China policy in his first term was placing tariffs on some Chinese goods. Mr. Biden and his aides kept those while expanding policy along three major prongs: strengthening alliances and creating new security partnerships in the Asia-Pacific region; limiting technology exports to China; and jump-starting industrial policy in the United States.

In short, Mr. Biden sought to turn China policy into global policy.

During Mr. Biden’s tenure, already-tense relations plummeted when House Speaker Nancy Pelosi visited Taiwan, the de facto independent island that China claims as its territory, and a Chinese spy balloon drifted over the United States. But his team scrambled to restart high-level communications, including between the two militaries.

The United States and China “are competing, obviously competing vigorously, and yet still the relationship has an element of stability so that we’re not presently on the brink of a downward spiral,” Jake Sullivan, the White House national security adviser, said in an interview in a West Wing conference room.

“That is a significant evolution over four years for how the relationship is managed on both sides,” he added, using the acronym for the People’s Republic of China. The Chinese Communist Party, he said, has now accepted the Biden team’s framing of “managed competition” for the relationship.

The Biden administration was animated by the idea that China wants to displace the United States as the world’s dominant power, said Rush Doshi, a China director who served on the National Security Council earlier in the Biden administration. Many Republican lawmakers and policymakers share that view.

Coming into office, Mr. Biden and his aides saw huge gaps in critical areas, including the U.S. defense industrial base, Mr. Sullivan said.

The administration set up two “big tent poles” of policy, as he put it: investments aimed at rejuvenating American manufacturing, technology innovation and supply chains; and investments in alliances and partnerships, “so that we broaden China strategy to really be a regional and global strategy.”

Mr. Sullivan pointed to alliances not only in Asia, but in Europe as well. Mr. Biden’s team helped persuade European nations to back away from some commercial agreements with China, and NATO to make stronger pronouncements on China and to signal support for Taiwan.

China’s partnership with Russia during President Vladimir V. Putin’s full-scale invasion of Ukraine has helped push the Europeans in that direction, as have China’s cyberespionage efforts.

But the trans-Atlantic allies have not gone as far as the United States in viewing China as a threat. Some European politicians still prioritize trade relations with China, the world’s second-largest economy. And Mr. Trump’s antagonizing of European nations could jeopardize the Biden administration’s work.

Moreover, U.S. allies could run into the arms of China if Mr. Trump makes good on his threat to impose universal tariffs even on them.

Mr. Trump also says allies are leeching off the U.S. military, and that they must pay the United States for protection or fend for themselves. In Asia, this thinking would apply to Japan, South Korea and the Philippines, as well as to Taiwan.

The Biden administration has had the opposite attitude. In creating a web of new security agreements among U.S. allies in Asia, it tried to make their militaries more intertwined with each other and with that of the United States — which, according to Mr. Biden’s team, would help deter China.

Mr. Biden also moved to bolster the military capacities of several allies and the U.S. military presence in Asia: sending Tomahawk missiles to Japan; working with Britain to start equipping Australia with nuclear submarine technology, and the submarines themselves; and expanding the U.S. military’s access to Philippine bases near Taiwan.

In private conversations in Washington, Chinese officials complained that it was a policy of containment.

A central question, difficult to answer and relevant for Mr. Trump’s team, is whether the Biden administration struck the right balance between deterrence and provocation. Is China accelerating its military buildup, and is it becoming more aggressive in the region, because of the American moves in its backyard?

Beijing took notice when Mr. Biden said on four separate occasions that the U.S. military would defend Taiwan in the event of a Chinese invasion.

Jessica Chen Weiss, a professor at Johns Hopkins University who worked briefly in the State Department under Mr. Blinken, noted that the administration’s policies didn’t ignite conflict, and that some of its diplomacy helped.

“It was able to avoid the extremes,” she said. “Whether or not that muddling through was ambitious enough to arrest the underlying tendencies remains to be seen.”

In summits, Mr. Xi directly criticized a signature Biden policy that Chinese officials insist is part of the containment effort: export controls imposed on advanced semiconductor chips, including the kind needed for developing artificial intelligence.

After rolling out the first tranche in 2022, Mr. Sullivan described it as a policy of keeping “foundational technologies” out of the hands of rivals by establishing a “small yard, high fence.”

Some experts argue the policy has backfired and has actually pushed China to accelerate innovation. And the less Chinese companies rely on American technology, the less leverage the United States has over China, they say.

Mr. Sullivan said that criticism “gets the chronology wrong.”

“Our semiconductor export controls were actually a reaction to China’s very overtly, very systematically stated policy that they were going to indigenize their semiconductor manufacturing capability,” he said.

Some former officials point to other policy shortcomings. Ryan Hass, a China director on President Barack Obama’s National Security Council, listed three: Mr. Biden and his team lacked a serious trade agenda for Asia, appeared timid in dealing with China, and seemed more comfortable interacting with advanced democracies on China policy than with developing nations.

But overall, he said, the policy worked: “America is in a stronger competitive position vis-à-vis China than it was when Biden entered office.”