I'm not confused. I first read Appendix I of the AD&D PHB 40 around 40 years ago. As
@Cadence has pointed out, it expressly states that psionics are an option, to be included if the Dungeon Master so decides. In this respect it is no different from the Bard.
I don't really understand what your point is, in insisting that psionics are "core". The rulebooks in which the relevant rules are presented both describe them as optional (as per
@Cadence's post). It is notorious that many if not most play groups did not use them. They are a largely peripheral mechanical system.
I don't think the comparison to 5e feats is remotely plausible or illuminating. Feats are a PC build element that introduce additional complexity, and detail/specification, into the build of any PC. They are optional, but they are widely used.
Psionics is simply an extra type of magic power that can be tacked onto any human, Dwarf or Halfling PC, with little rhyme or reason, based on a rather arbitrary roll of the percentile dice. There is a good reason they are in an appendix, whereas (for instance) spells, equipment, ability score charts, etc are not.