The opinion in Loper Bright Enterprises v. Raimondo is unlikely to have much application to the FAA regulations that apply to us in flying and maintaining our Mooneys.
The holding in Loper Bright is that judges should be the arbiters of what a statute means and that a judge need not defer to regulations that purport to interpret a statute even if the statute appears to be ambiguous (although if the statute gives a specific grant of regulatory authority and that grant is constitutional, Loper Bright says that the proper interpretation of that statute is to enforce the resulting regulation). I'm a tax lawyer, not an aviation lawyer, and I can name a lot of regulations promulgated under the Internal Revenue Code that may be subject to challenge under Loper Bright. One reason for that is that there are a lot of statutes in the Internal Revenue Code, so there is a lot of statutory language for judges to interpret.
Contrast that with Part 91. The authority the FAA cites for promulgating Part 91 is far more general than the Internal Revenue Code. It's just a handful of statutes: 49 U.S.C. 106(f), 40101, 40103, 40105, 40113, 40120, 44101, 44111, 44701, 44704, 44709, 44711, 44712, 44715, 44716, 44717, 44722, 46306, 46315, 46316, 46504, 46506-46507, 47122, 47508, 47528-47531, 47534; Pub. L. 114-190, 130 Stat. 615 (49 U.S.C. 44703 note); Sec. 828 of Pub. L. 118-63, 138 Stat. 1330 (49 U.S.C. 44703 note); articles 12 and 29 of the Convention on International Civil Aviation (61 Stat. 1180), (126 Stat. 11). The statutes tend to contain broad regulatory grants of authority. For example, section 40103(b)(2) provides:
"The Administrator shall prescribe air traffic regulations on the flight of aircraft (including regulations on safe altitudes) for— (A) navigating, protecting, and identifying aircraft; (B) protecting individuals and property on the ground; (C) using the navigable airspace efficiently; and (D) collision between aircraft, between aircraft and land or water vehicles, and between aircraft and airborne objects."
If you run afoul of the regulations that apply to buzzing your neighbor's house, you're not likely to have much success pointing to Loper Bright and saying that the regulations are not "law" because they are not the best interpretation of this statutory language.
I'm not saying that there can be no challenges to FAA regulations under Loper Bright. Congress did set out specific statutory rules regarding ELTs, and enforcement via civil and criminal penalties, and a short list of other topics. But I would be very surprised if Loper Bright could be wielded to challenge most of the regs that apply to us.