So I just caught my Android in the process of breaking; it went off, made no noise, "getting called" animation was showing on the screen, but swiping up did nothing, it just bounced back down and didn't pick up the call. Didn't matter how often I tried.
So yeah, it's definitely just the phone app that's fucked.
I am clearly not the only one with this problem: https://support.google.com/pixelphone/thread/144103327/unable-to-answer-calls-when-phone-rings?hl=en
@freakazoid My phone is not a Pixel, no.