So you're saying ADS-B sends GPS altitude not barometric altitude. Well I've just learned something.
No, that is what ICAO reference has stated, and it states that they broadcast both....
Barometric altitude is used for air traffic separation and must be corrected for pressure/temperature. Geometric altitude is what the GPS system provides, and is what RNAV avionics use, and many ATM systems that use the broadcasts...
The system on the aircraft has to be able to calc the differences between the ellipsoid, the geoid, and the measurement. This why there are calculations in the fms. The GPS system in the ac references the WGS84 ellipsoid. Procedure designs use this as the basis for the altitudes for the coded procedures.
Note Australia has a very unusual geoid-ellipsoid seperation, so this must be taken into account in the designs that rely on GPS navigation (like WAAS/GBAS)
-35m to +75m correction...
As shown on this representation, a GPS that uses an approx value for lat/long, depending on the internal grid size, could be off quite a bit...
then there are the studies...
Findings showed obvious variation between the altitudes during different phases of flight. The barometric altitude displayed higher readings than geometric height while the aircraft is cruising. The discrepancies between the two altitudes were bigger during the climbing phase. It is also found that the absolute difference between geometric height and barometric altitude ranges from 25 feet – 1325 feet with an average of 569 feet.
Just to note, GLONASS, of course, uses a different ellipsoid....