What additional US-power or ICAO requirements apply to a departing US-based crew with a US-registered aircraft flying to land in Mexico? What are additional requirements (equipment, licenses, identification, etc.) for a flight operation with a US-based aircraft and crew leaving the US to enter and land in Mexico that are imposed on the operation by the US authorities such as the government or any of its agencies and comprehensive international agencies such as ICAO?

This differentiates from similar questions because I am not asking about the governing set of laws in international territory or what laws of a different country than the home country would apply to the flight; of course ICAO is international in all cases so could be applied as valid in any home country that an aircraft may depart from.  Each other, non-US, country's specific laws may vary, so they are removed from the scope of my question.
The only aviation-related requirements on crossing the US border are:


All flights crossing the US's Air Defense Identification Zone (ADIZ) in either direction must be on an IFR or DVFR flight plan, talking to ATC and have a discrete transponder code.
A list of all passengers and crew must be filed with eAPIS at least 24 hours before crossing, in either direction, and the plane must have an eAPIS decal.


The only difference between leaving vs entering that I'm aware of is that you don't need to leave from a designated port of entry. (Some other countries do require that.)

As a practical matter, there are a handful of aviation-related things that apply to most/all other countries that US pilots don't have to worry about in the US:


The pilot(s) must have ICAO-recognized license(s). FAA Student, Sport and Recreational licenses are not.
The pilot(s) must have appropriate medical certificate(s). No BasicMed.
The aircraft must have a normal airworthiness certificate. No experimental aircraft.
The aircraft and at least one pilot must have FCC radio licenses.


Technically, you don't need passports to leave, but you'll need them to go anywhere else (and to return) by air, so they are effectively required for both.

There are thousands of other laws that apply to all people or goods leaving the US regardless of mode, such as not exporting restricted technology or weapons, human trafficking, fleeing prosecution, etc.  (And there are even more for entering.)  I doubt anyone could list them all, and that is probably off-topic anyway.