I’ve gotten several comments deriding me referring to an Elizabeth Line station as “a tube station” but so far—despite my requests—nobody’s explained WHY.

Is it NOT considered part of the Underground?
It has the same logo but in purple, which I assumed was just for Queen reasons.

It interfaces WITH Underground stations, does it not??

Is this a colloquialism I just won’t understand?

@Graham_LRR I think simply for many "The Tube" is just The Underground proper. The Elizabeth Line is run by TfL and has a purple roundel, which makes it another of what TfL calls a mode, like Underground, DLR, Overground, Buses, etc.
Design standards

We have produced a range of design standards for use by staff, suppliers and design agencies involved in graphic design and layout.

Transport for London
@rakslice OMG yes, thank you for this!!

@Graham_LRR In particular "Roundels" https://content.tfl.gov.uk/tfl-advertising-standard.pdf#page=8

Hmm... what is "TfL Rail" there? Well, it's actually a whole separate brand they created to use for the train services they were taking over that were going to become part of then Crossrail, for the 7 years before the central part was ready, presumably just so they could avoid spoiling the final brand before the whole line was ready
https://en.wikipedia.org/wiki/TfL_Rail