While Twitter’s stock price has held up because of Mr. Musk’s potential acquisition, its performance has declined. The company reported a surprising decline in revenue in the second quarter that it blamed on weakness in the advertising industry and uncertainty related to Mr. Musk’s acquisition.

Twitter this year is expected by analysts to report one of its slowest annual rates of sales growth ever as a public company, at 4.5%. In 2021, revenue rose 37%.

Mr. Musk has given few specific details about his plans for Twitter, but the billionaire chief executive of

Tesla Inc.

has said he wants to transform Twitter as a private company and unlock what he called its extraordinary potential as a platform for free speech.

He has talked about modifying Twitter’s rules around content moderation, reducing its reliance on advertising—which provided more than 90% of its revenue in this year’s second quarter—and making Twitter’s algorithms open source, which would allow others to view and recommend changes. Mr. Musk also has proposed “defeating the spam bots and authenticating all humans.”

In texts released last week as part of the litigation between Twitter and Mr. Musk over his effort to abandon the deal, Mr. Musk said in April that his biggest concerns were Twitter’s head count and expense growth. He also said he wanted to oversee software development at Twitter and works better with engineers than people with business degrees.

There are no guarantees that Mr. Musk will follow through with his proposal and close the transaction. Mr. Musk and Twitter are scheduled to go to trial Oct. 17 in Delaware over his effort to abandon the deal, and that could still go forward.

On Wednesday, the Delaware Chancery Court judge presiding over the legal battle said she is pressing ahead with preparing for the trial and issued a ruling that asked Mr. Musk’s legal team to produce more of his text messages to the extent they haven’t done so already.

Should a deal occur and avert a trial, the resolution could ease some of the uncertainty surrounding the company’s future.

“Assuming the deal closes, it’s a good price for shareholders,” said Jason Goldman, former Twitter product chief and board member. “But it’s a bad outcome for everyone else,” including employees who have labored under the uncertainty and users who rely on the product, he said. Mr. Goldman said he didn’t think Mr. Musk has presented serious ideas about how he would lead such an influential platform.

Mr. Musk has proven doubters wrong before in becoming the world’s wealthiest person. He has turned Tesla into the world’s most valuable car company and a leader in electric vehicles, and his SpaceX company is the world’s busiest rocket-launch operation.

Mr. Musk’s legal team declined to comment Tuesday about his proposal. Twitter on Tuesday confirmed receipt of Mr. Musk’s letter and said it intends to close the transaction at the original price of $54.20 a share.

The outlook for the social-media industry has darkened in recent weeks.

Snap Inc.

in August said it was slashing one-fifth of its workforce and curbing investment in a range of areas after a slowdown in its business. Facebook parent

Meta Platforms Inc.

last week told employees it was implementing a hiring freeze and looking for other ways to cut costs.

In July, Twitter said in a regulatory filing that attrition was slightly higher than in normal economic times, but remained in line with current industry trends. Twitter said Tuesday that it had anticipated higher attrition this year even before the merger agreement.

In addition, Twitter’s former head of security,

Peiter Zatko,

emerged in August with a whistleblower complaint listing a litany of criticisms about the company’s management of security and privacy issues. That complaint prompted new scrutiny from Washington lawmakers. Twitter CEO

Parag Agrawal

told employees in a memo at the time that the spotlight on Twitter would “only make our work harder.” Twitter also said that Mr. Zatko’s claims were inaccurate.

Despite the industry’s challenges, Twitter said in July that its audience has grown, reporting a second-quarter average of 237.8 million monetizable daily active users, up 17% from the same period a year earlier. Advertising revenue increased 2% in the second quarter compared with the year-earlier period.

Mr. Musk, when he met with Twitter employees in June, was asked about what he would consider successful for Twitter five to 10 years from now, and said a substantial increase in daily active users to over a billion, according to people familiar with the meeting. He also said during the meeting that Twitter should be entertaining, like TikTok, and that he admired the Chinese app

WeChat,

which is used heavily in China for a range of purposes including e-commerce and social networking.

Asked about his stance on free speech, Mr. Musk drew a distinction between freedom of speech and freedom of reach, according to attendees. He said that meant people should be allowed to say pretty outrageous things within the law but didn’t necessarily deserve to have their tweets amplified and spread virally across Twitter.

In the texts released last week, Mr. Musk said in April, “Twitter is obviously not going to be turned into some right wing nuthouse. Aiming to be as broadly inclusive as possible.”

Accomplishing that balance will be a challenge, content-moderation analysts said Tuesday.

“Elon Musk and his new leadership are about to get a crash course in the complexities of moderating harmful content,” said Eddie Perez, a former Twitter employee who worked on civic integrity and misleading information and is a board member at the OSET Institute, a nonpartisan election-technology group.

Write to Alexa Corse at alexa.corse@wsj.com