So again, they're going to argue in court that the entire free market system requires a law ordering somebody to disclose a price for every good and/or service exchanged in this country. Again, good luck with that.

What? No. Why would they argue that?

They would simply argue that the PPACA does not specifically authorize HHS or CMS to require that insurance plans make public their reimbursement rate agreements with providers. They weren't required to do that prior to the PPACA, and the PPACA doesn't specifically require them to do it. The PPACA just has a "catch-all" allowing HHS to require disclosure of other information not specifically provided. It's not a particularly unusual argument for them to claim that the catch-all should not be construed as Congress having decided that this information needs to be made public under Obamacare, and I think the courts will be sympathetic to it. None of that has anything to do with "the entire free market system."

Even if that regulation were upheld in court it still doesn't do what I think you want the EO to do, which is to require providers to say how much procedures cost. Because even under the PPACA, it doesn't require the actual providers to disclose prices. It just requires insurance companies to disclose how much they will cover.
Hospitals above a certain size already are supposed to disclose, but the PPACA doesn't expand that to any other providers. And as mentioned, that disclosure requirement is already inadequately enforced - and will be even more inadequately enforced once DOGE takes Musk's chainsaw to CMS.