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But The New York Times found that hundreds of other posts commissioned by the campaign, many of them focusing on hot-button issues like data centers, Flock cameras and affordability, do not disclose that they were paid for.

Ms. Hinojosa’s campaign said Texas regulations did not require the disclosures because it had paid a third-party social media firm to oversee the effort and had not approved each post.

Legal experts say the failure to disclose the advertisements might run afoul of the regulations. Both the campaign and the content creators could be on the hook for penalties as high as $4,000 for violating the disclaimer requirement; the state rule, adopted in 2024, doesn’t detail exactly who is liable. The Texas Ethics Commission, which oversees campaigns in the state, did not respond to a query.

“There’s no way that holds up to scrutiny,” said Andrew Cates, an elections lawyer in Austin. “It’s simple: You don’t have to have a disclosure statement on posts if you weren’t paid for it, but if you were, you do.”

The lack of disclosures shows how, in a time of rapid technological change, even regulations designed to force politicians to acknowledge paid digital political messaging have had limited effect.

As an increasing share of the public ignores traditional political advertising, campaigns across the country are pouring millions into efforts to reach potential voters on the internet. But while TV ads, billboards or mailers must, by law, carry disclaimers stating who paid for them, only Texas and California have transparency rules governing political ads on social media. And those laws apply only to statewide and local races, not federal ones.

Texas is home to some of the most hotly contested and expensive campaigns in the nation this campaign cycle, making the murky questions swirling around online transparency particularly salient.

Ms. Hinojosa’s campaign paid a social media marketing firm, Politiclip, $150,000 for “news clipping services,” according to campaign finance filings.

Like other clipping companies, Politiclip recruits large numbers of creators to blast out content, amplifying scripted narratives in a way that appears organic to the algorithms controlling social media feeds.

Screenshots of internal Politiclip data reviewed by The New York Times show that it approved more than 550 posts supporting Ms. Hinojosa or opposing Mr. Abbott through the first week of October. Some content creators recruited by the firm were offered a rate of $3 per 1,000 views, the screenshots show.

Ari Salzberg, who said he founded Politiclip in April, declined to comment, saying he deferred to the campaign on the disclosure issue. Ms. Hinojosa’s campaign director, Amy Friedman, said Politiclip did not consult directly with the campaign on which accounts it recruited or seek its input on the posts it made.

“We hired a firm to help grow Gina’s audience and name ID, and had no authorization of the posts in question,” Ms. Friedman said in a statement. The campaign based its reasoning on language in the regulation stating that only content “authorized by a candidate, an agent of a candidate or a political committee” triggers the disclaimer requirement.

Ms. Friedman noted that the campaign had hired a different social media marketing firm to work with a separate set of influencers who posted with “the campaign’s explicit authorization and approval” and that those creators were asked to include disclaimers noting they were paid.

An Instagram post from a fitness influencer, Benny Porras, who has 265,000 followers on Instagram, featured him alongside Ms. Hinojosa and included a badge reading, “Paid partnership with ginafortexas,” for example.

Brandon Rottinghaus, a political science professor at the University of Houston, questioned the logic of treating two sets of paid posts so differently. “If campaigns can avoid transparency requirements by simply hiring outside consultants to run the messaging, it creates an enormous and unintended loophole,” he said.

Politiclip’s work has garnered disclosures elsewhere. Content creators recruited by the firm to post in favor of Nithya Raman, a candidate for Los Angeles mayor, have been including disclaimers in their posts, as required by California law. To date, Ms. Raman’s campaign has paid Politiclip $100,000, filings show.

In July, Politiclip was paid $25,000 by Fighting for Michigan, a super PAC supporting Abdul El-Sayed, then seeking the Democratic nomination for Senate in that state. Creators recruited for that effort also included disclosures on their posts, even though, because it was a federal campaign, there was no legal requirement to do so.

Some of the creators made posts in all three of those races, The Times found. The posts about Ms. Raman and Dr. El-Sayed included disclosures; those about Ms. Hinojosa did not.

An anonymous account with the handle @askablkman, for example, disclosed being paid by both Fighting for Michigan and Ms. Raman’s campaign when it posted on their behalf. The account, which has 274,000 followers on Instagram, has posted at least 22 times supporting Ms. Hinojosa or critiquing Mr. Abbott. None of those included disclosures.

The account did not respond to requests for comment, but after The Times sent an inquiry, all 25 posts that it had identified were deleted.

Mr. Salzberg did not respond to a query about whether that account was part of Politiclip’s paid campaign.

Republicans in Texas also appear to be benefiting from coordinated social media campaigns, though it is not clear whether they are part of a paid effort and, if so, who is paying them.

The clearest example concerns Ken Paxton, the Republican attorney general, who is running for Senate. In late August, a string of nearly identical posts began popping up on Instagram supporting him.

The posts, which came from a dozen accounts, promoted an effort by Mr. Paxton to shut down a real estate project in Kaufman County, near Dallas, funded by a Dubai-based developer.

One of those accounts, which has 1.2 million followers and uses the handle @republicanparty, included a revealing addendum to its caption: “#ad.” The post has been seen more than 57,000 times. A separate post from the same account, one of several identical posts praising an effort by Mr. Paxton to close what it described as a “Chinese birth tourism center,” contained the text “#sp” — short for “sponsored,” in social media parlance. That post has 124,000 views.

The hash tags suggest that the posts were part of a paid and coordinated effort, a possibility underscored by the fact that the account and at least six of the others making the copycat posts backing Mr. Paxton are listed by LLM/DCW Media, a separate website that offers to place content on 3,000 vetted Instagram pages for a fee.

There are no federal rules requiring disclosure of paid political content on social media, and Nick Maddux, a spokesman for Mr. Paxton’s campaign, said the campaign had no involvement.

“Ken Paxton for Senate is not paying anyone to do with what you are claiming is occurring,” he said, adding that he had no idea who might be behind the posts.

Messages to the @republicanparty account, which notes in its Instagram bio that it “is not the official account for the Republican Party,” went unanswered.

A number of the accounts that made the pro-Paxton posts about the Dubai-based developer’s real estate deal have also posted in support of Mr. Abbott, as have more than two dozen other accounts that are listed in LLM/DCW Media’s catalog.

One account with 1.2 million followers on Instagram posted in support of Mr. Paxton more than 30 times and Mr. Abbott more than 15 times from June through October.

LLM/DCW Media, which describes itself as “one of Instagram’s largest A.I., tech and business networks,” did not respond to a request for comment. A spokesman for Mr. Abbott’s campaign also did not reply to a query; the governor’s campaign finance filings do not reveal any direct payments to companies that manage social media campaigns.