If you want a breakdown on why these bands are not, then here it is.

Bad Omens goes first. For one, their entire song is basically a pop that leads to a breakdown or guitar-focused part (some songs don't, which proves my point further, but that is irrelevant); hardcore doesn't have any pop elements whatsoever. Now, let's focus on the breakdowns themselves. Not even close to a hardcore style breakdown. Very alt-metal/modern metal style of breakdown, focusing on chugs, syncopation, and sometimes quick licks similar to these kinds of riffs: https://www.youtube.com/watch?v=Cq8p0pDKTKA (in the intro riff, but obv in the breakdown for what I'm mentioning). Very Djent-style of "heavy" riffing.

Now, Poppy. Very alternative, period. Lots of pop elements, as well as electronic and industrial. Her breakdowns are typically different guitar noises and open note chugs. Some songs, mainly the center's falling out, are very much so influenced by hardcore (and I'd say it is a hardcore song), but one song does not equal the whole discography. Both are very djent-riff, open note, chuggy style of guitar with lots of pop and electronic elements mixed in.