I tried the tapping a bit more, and now the red gun also has this problem... I
didn't tap that hard I think (from the description "not enough to break it,
but close" I would think I need to tap a lot harder).

Now my question is: are those cathodes/filaments so fragile that I could have
damaged them, or is it possible I dislodged dirt which now also affects the
red gun?

The filaments were cold BTW, when I tried this. I suppose warm filaments are
more easily damaged.