It’s hard to find knowledgeable people on this topic,
but you sound like you know what you’re talking about.
That's just because I'm quite able to sound cleverer than I really am.
But yeah Apple's earbuds are lacking bass extension and show quite a lot of person to person variability :
https://www.rtings.com/headphones/reviews/apple/earpods
The APM's response is for the most part more linear and more stable at lower frequencies (Adaptive EQ helps) :
The Apple AirPods Max Wireless are Apple's first pair of wireless over-ear headphones. Unlike other headphones from Apple, like the Apple AirPods Pro Truly Wirel...
www.rtings.com
I personally find the measurements made by Jude at Head-fi to be more representative of how the APM sound to me :
Fig.1 (above): Apple AirPods Max frequency response, average of three seatings. Fig.1 (above): Apple AirPods Max THD (total harmonic distortion) at 90 dBSPL, 100 dBSPL, 110 dBSPL. The measurements in this post were made using: Brüel & Kjær High-frequency Head and Torso Simulator (HATS) Type...
www.head-fi.org
In all cases it's important to not over-interpret headphones measurements and take them with a pinch of salt.
Rtings's articles are a good primer on headphones measurements :
https://www.rtings.com/headphones/tests
And this article on what sort of research has been going on in the last 10-15 years in regards to what a decent frequency response is for headphones :
In Part 1 of the Harman Target Curve deep-dive series, we explore the fundamental of human hearing and how it is related to the Harman Curve.
www.headphonesty.com
Measuring compression codecs, either as a file format, or as wireless audio over BT, is very difficult for mere mortals, but blind A/B tests can be performed.
https://en.wikipedia.org/wiki/Codec_listening_test
In regards to AAC 256kbps as a file format, most people are unable to discriminate it from a lossless file.
But it seems that, for some compression formats, provided the right circumstances, some people
may be able to A/B it if they know what to look for.
codecs for wireless audio are a different thing, even though in regards to AAC it shares similar underpinnings as the file compression scheme. Some implementations of wireless audio can produce easily audible artefacts, and sometimes it's not even a question of codecs. But so far with my AirPods I haven't noticed significant red flags.
All in all I don't think that the benefits one could gain from lossless files and wired connection would compensate for the earbuds' frequency response shortcomings vs. the AirPods Max.