Just copying the actual newspaper part here:

(B) Advertisements in newspaper or professional journals.

(1) Placing an advertisement on two different Sundays in the newspaper of general circulation in the area of intended employment most appropriate to the occupation and the workers likely to apply for the job opportunity and most likely to bring responses from able, willing, qualified, and available U.S. workers.

(2) If the job opportunity is located in a rural area of intended employment that does not have a newspaper with a Sunday edition, the employer may use the edition with the widest circulation in the area of intended employment.

(3) The advertisements must satisfy the requirements of paragraph (f) of this section. Documentation of this step can be satisfied by furnishing copies of the newspaper pages in which the advertisements appeared or proof of publication furnished by the newspaper.

(4) If the job involved in the application requires experience and an advanced degree, and a professional journal normally would be used to advertise the job opportunity, the employer may, in lieu of one of the Sunday advertisements, place an advertisement in the professional journal most likely to bring responses from able, willing, qualified, and available U.S. workers. Documentation of this step can be satisfied by providing a copy of the page in which the advertisement appeared.

I'm more speaking to the point that the options are "newspaper or professional journals" in the-year-of-our-lord 2026. Job sites are under a section that gives a pool of other options of which the employer must pick three. Those requirements should be flipped (job sites are the requirement, newspaper and journals are one of the extra options) if the DoL wasn't asleep at the wheel.

Edit: And thats not a R vs D thing. The requirements have been this way under multiple administrations, and newspapers have not been a primary way of sourcing candidates for two decades.

Oh I completely get the point that it's an out of date practice. However, it is the current rule. You can't say that it's only these specific companies that do that. Every company that files for employment-based green cards does this. Yes, if the government wants to change that then they should change the actual rules, not just try to guilt companies into doing something different.

Not an American, but why Sundays? I'd assume job seekers wouldn't care as much on Sundays

Going back in time it's likely because the Sunday paper was traditionally the largest edition of the week. It would normally have a lot more sections to it. You'd have special features like the Sunday comics and they would be in color, not black & white like the rest of the week. The paper would usually be a bit more expensive as well ie. $2 instead of $1. I'm guessing it likely reached a larger audience.

lol, I feel old now talking about this :)

This made me look up when the rules about posting in the newspaper went into effect. I was surprised to find that it was 2005. This is much later than I thought. I would have guessed the 90s. By 2005, it was clear that the newspaper industry was dying due to the internet. I guess this is one example of how out of touch government can be.

Someone else mentioned in the thread elsewhere about whether the rules would need Congressional approval. Gemini says that these are purely an agency regulation and the Department of Labor can update them at anytime. It's kind of mind-boggling that no administration has updated them in 20+ years.