BP is (for clinical purposes) a syndrome. So "duck-typed".

It being the alcohol all along doesn't really matter (it does very much for scientific research, so use of the substance-induced bipolar diagnosis is probably best, but maybe not for acceptance). It is however unlikely to be a sufficient factor/cause. Likewise, it being largely due to anxiety doesn't make it more or less BP.

I very much believe BPD to be ameliorating/reducing factor in BP, so that BP may be completely neutralised by BPD.

So BPD, anxiety, substance-use and the BP syndrome give a better measure of the underlying problems characterised by BP.

Edit:
There is probably one underlying problem, with a certain strength, but with one or more genetic and/or biochemical problems/differences underlying it, resulting in different strengths, as well as personality reducing the problem and/or making it worse and substance-use and anxiety making that problem worse. It is possible, not unlikely, the shared cause is cell damage and reduction.

Anxiety is more complex, there being more primary and secondary anxiety and a distinction should be made.