Applications engineers (I don't know what "PAE" is, but "FAE" I do)
have the unfortunate role of dealing with angry, confused and
clueless customers (the happy and cognizant ones don't need
to call you). If you always wanted to be a kindergarten teacher
with a soldering iron, maybe it's for you. If you don't suffer
fools and their whining with a smile, it's surely not.
I had to do backup applications support for any chips I designed.
That's just how it was. Central Apps answered the phone and
sent out literature. Any detail questions always had to go back
to the designer until CentApps recorded the answer "for next
time".
You might inquire about career progression from this point
onward. If (say) it was a stepping stone to product design,
you might like it. If it's a stepping stone to "sit in the cubicle
and answer idiots' phone calls for the rest of your career",
maybe you wait for the next opportunity. In the middle,
can a deal be made? Like, you agree to the PAE role -if-
you also get entry level design work as part of your declared
role. If that was an interest and if the management was prone
to honor agreements. Then when you've got some design work
under your belt you can make a lateral move to a position
where you get to do what you really want.