Some things to know about executive orders:

[Ocelot II]

32. Here's a good analysis of the situation:

This writer thinks their removal was probably lawful, and explains why, but goes on to say:

The IG removal issue is not the biggest of deals, since President Trump had clear statutory authority to remove the IGs if he had provided the easy-to-satisfy substantive rationale and thirty days notice. The much more important issue concerns who replaces the removed IGs. On this issue the 2022 IG law has more bite. The law narrows the definition of the “first assistant” who, under the FVRA, presumptively takes over for the removed IG. It also authorizes the president to replace the first assistant only with another Senate-confirmed IG or a GS-15 or higher employee who was in office for more than 90 days during the year prior to the vacancy.

The practical bottom line is that a career official high up in the office of each IG will by law become the acting IG, and Trump can replace that person only with someone already in the IG cadre.

We do not yet know how Trump plans to replace the fired IGs within these constraints. He might nominate new IGs, but they must be confirmed by the Senate, and that likely will not happen this year. The important question is thus whether Trump can find a lawful and congenial replacement for the first assistant under the 2022 law.

https://www.lawfaremedia.org/article/trump-fired-17-inspectors-general-was-it-legal