That was it, an indexing problem. Thank you very much. I didn't know that Eclipse used two different, possibly inconsistent, methods for resolving symbols and functions.
My next steps are to get an ESP8266 example working, demonstrate that I can export a project in such a way that someone still using the Arduino IDE can use it, then migrate my current development to Sloeber. It is 3000+ code lines and more compilation unit tabs than can fit on the Arduino IDE Top bar ! Anyway, I try to sort all that out myself.