I worked in the semiconductor industry, and at least in our niche of the semiconductor industry, FAEs were some of the worst paid people, a long with production test for some reason.
FAEs were seen as the lowest level support who were a stop-gap for our application engineers (non-field). If a big customer had a problem, we would send an AE out to show that we were taking it seriously. No idea if it's the same in other industries though. Application engineers weren't that we'll paid either.
Technical marketing and sales were paid well, but maybe this is a just a title thing (what you called FAE is what we called sales/marketing). Their salaries were predominantly sale/deal based bonuses though.
For people that actually developed the chips, analogue designers were the highest paid followed by digital designers. Then digital verification engineers, with verification engineer salary increasing very quickly. The salaries were shit compared to software though.
But now, talking to my friends still in the sector(doing design), competition is absolutely fierce and their salaries are increasing rapidly along with getting a lot more shares. There was a point where a senior analogue engineer could move to a graduate software position and make more money. Those days are gone now, and salaries are pretty close.
A friend interviewed for a hardware position at Apple and the salary was definitely SWE levels of high.