That is an exclusive back door deal with both Google and Apple, that was likely only created because of how much antitrust pressure they were under. Times are changing, I wouldn't be surprised at all if Apple backs out of the deal over time.

they mean that you can pay for spotify without it being through the app store or play store, meaning that Apple and Google can't take a cut, meaning that it's cheaper.

that's not some kind of deal, that's just how it works.

There was never a “back door deal”. Very few of the subscription streaming services allow in app purchases.