from BW
I left out the critical word of "internal" as well. If the challenger is from outside it is UW.
We have an External Power which supports one of two Internal Powers (say "Power B"). To the External Power, it is waging UW vs Power A (and vice versa). However, Power A still could regard Power B as an "insurgent" and as a Power in a non-international armed conflict. Sorta Vietnam, ain't it ?

The UW conflict could be an international armed conflict if both the External Power and Power A are states. Your example of AQ (IMO: agree that AQ as a TVNSA wages UW, not a "global insurgency", using inter alia domestic insurgencies as tools) vice a state Power would be a non-international armed conflict, since AQ is not a nation-state and has neither accepted nor applied the 1949 GCs (as required by Common Article 2).

My other questions and comments still apply from the post above.

Regards

Mike