I can’t argue the current usage as I’m not terminally online enough anymore to have that knowledge but the original online usage of red-pill and ‘redpilling’ somebody was absolutely intrinsically connected to far-right and incel online spaces.

When you say it “developed across the whole internet, not just within incel communities” this is evidentially wrong. Early use was based around 4chan and manosphere/MRA ‘gender-truths’ and then increasingly co-opted by the alt-right pipeline to invoke a rejection of what they saw as the liberal status quo. Redpilling in its early use was basically slowly radicalising somebody to extreme alt-right viewpoints.

It’s one of the phenomena of linguistic appropriation (matrix redpill & trans-identity notions -> right-wing appropriation, gender standards and conservative values -> wide-spread normalization also outside strictly political contexts) by the right that words like woke, privileged also went through.