When to descend

don't have to request lower from ATC, clearance for the approach
authorizes me to descend to 2700 at the TAA boundary.


I'm with Mitty on this one. AIM Section 5-4-5.d.4(b) Says:

"Pilots entering the TAA and cleared by air traffic control, are
expected to proceed directly to the IAF associated with that area of
the TAA at the altitude depicted, unless otherwise cleared by air
traffic control."

If the clearance was indeed "...maintain 4000 until established" that
would fit the "..unless otherwise cleared by air traffic control"
clause.

To put this to a test, ask yourself when would you report established
on the approach if asked by ATC to ".. report established on the
approach"? My answer would be when I'm on one of the depicted
portions of the approach and not the TAA.

I guess one could argue that the TAA is a depicted portion of the
approach but I can't find any official publication pointing to that
fact.