To some Ukrainian forces, soldiers from the Wagner Group were the best-equipped fighters they had seen since Russia invaded last year. To others, it was their training that distinguished them: Ukrainian soldiers recalled battlefield stories of aggressive tactics or a sniper downing a drone with a single shot.

But after the short-lived mutiny led by the head of the group, Yevgeny V. Prigozhin, it is not clear whether Wagner will still be a fighting force on the battlefield with its fate now in question.

For now, the uncertain status of Wagner is bound to be a relief for Ukrainian soldiers. Though the front lines in Ukraine are likely to remain unchanged in the short term, depending on how events unfold in Russia, the Ukrainian military may be able to capitalize on the chaos and weakening morale to try to make some gains, according to independent analysts and American officials.

Still, it is too soon to determine the long-term implications of the feud between Mr. Prigozhin and the Russian military establishment, American officials said. In Bakhmut, Wagner played an outsize role in the campaign to take the eastern city, Moscow’s one major battlefield victory this year, and solidified an uneasy alliance with the Russian military — only to see the partnership break once the city was captured.

“The previous relationship between Wagner and the Russian government is likely over,” said Rob Lee, a senior fellow with the Foreign Policy Research Institute. “Even had this not happened, it was unclear if Wagner would have played the same role in this war as it had in the battle for Bakhmut.”

The intense fighting in Bakhmut led to huge numbers of Russians being injured or killed in the first months of this year, American officials said. In taking the city this spring, Wagner forces showed they had learned hard lessons from fighting over the last year, improving their tactics and making it far harder for Ukraine to mount a strong defense.

Wagner’s contract fighters outpaced Ukrainian defenders by using savvy maneuvers on the ground and sending wave after wave of prisoner conscripts into the fight.

But Bakhmut was a Pyrrhic victory for Mr. Prigozhin.

The city was not a prize many in the Russian military thought was particularly important. Its strategic value was further diminished when Ukraine’s military seized high ground on Bakhmut’s periphery, preventing Russia from using the city as a staging ground for attacks that could have led Moscow to take Kramatorsk, the next city it sought to expand its control of eastern Ukraine.

What’s more, the events that unfolded during and after Bakhmut’s capture seem to have precipitated the rupture between Mr. Prigozhin and Russia’s Defense Ministry.

Mr. Prigozhin’s forces were able to take the city center only after Russia’s president, Vladimir V. Putin, ordered the regular army to fortify Wagner’s troops to guard their flanks from attacks by the Ukrainians.

That influx of Russian troops was key to Wagner’s victory and reinforced the importance of the army. But Mr. Prigozhin may have learned a different lesson from the support he earned from Mr. Putin.

After seizing Bakhmut, the Russian Defense Ministry took steps to integrate Wagner into the broader military, which would have reduced Mr. Prigozhin’s power. When Russia forced all volunteers fighting in Ukraine to sign contracts with the ministry, it meant that Mr. Prigozhin would have had to put his forces under the control of the military, said Tatiana Stanovaya, a senior fellow at the Carnegie Endowment for International Peace.

“This is one of the reasons Prigozhin went mad,” Ms. Stanovaya said, “because he realized now he is out of Ukraine.”

Mr. Prigozhin became increasingly strident in his criticism of Russian military units after that, and U.S., British and Ukrainian intelligence began developing information that he might make an offensive move with his troops to force a change in the Defense Ministry. That intelligence was proved right on Friday, as Wagner troops moved to take control of a southern Russian city.

Just as quickly, the mutiny was over the next day, ending with the announcement that Mr. Prigozhin would halt his march on Moscow and accept exile to Belarus.

The Kremlin announced that Wagner troops who did not participate in the revolt would be allowed to sign contracts with the Defense Ministry. Those that had joined the convoy would not be prosecuted. The statement suggested that Wagner in its current form would no longer exist.

Though part of Mr. Prigozhin’s mercenary cadre is likely to continue under Russian Army control, how many Wagner soldiers would be willing to fight under the ministry’s umbrella is an open question.

Ukraine will surely look to take advantage of the chaos caused by Mr. Prigozhin, but there did not seem to be any immediate defensive gaps to exploit, according to American officials and independent analysts.

And Mr. Prigozhin’s march, at least according to a preliminary analysis, did not cause any Russian units on Friday or Saturday to leave their positions in southern or eastern Ukraine to come to Moscow’s defense, American officials said. While the drama was unfolding, there was no letup in the war: Russian forces fired more than 50 missiles across Ukraine before dawn on Saturday.

Wagner has been an incredibly important tool of Russian foreign policy, particularly in Mali, the Central African Republic, Syria and other countries. While the group will most likely be transformed under the Defense Ministry’s control, it is not certain that the Kremlin will let it fade away as an effective fighting force.

And, Mr. Prigozhin may also have some next move yet to play out.

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