How to add a payment gateway for app subscriptions without violating Play Store/App Store rules?

the gateway isn't the variable here. both stores care about where the purchase happens and whether the thing you're unlocking gets used inside the app, so routing checkout through a merchant of record doesn't create an exemption. swapping polar for something else changes nothing about the rule. sell the subscription on the web instead, fully outside the app. people make an account and pay on your site, then sign into the app and it just reflects the entitlement, no purchase flow on device ever. that's how most saas with a mobile app already run it, and it holds up regardless of which way the anti-steering stuff swings this quarter. also worth saying: if your country isn't supported for merchant payouts you can't take iap anyway, so web isn't the safer path, it's your only one. one gotcha, an app that requires sign-in with no visible way to get an account can get bounced in review as non-functional, so keep sign-in normal and just don't advertise or link the checkout. do go read the current guidelines yourself though, the external link rules have shifted a lot under regulatory and court pressure and anything anyone tells you here, mine included, goes stale fast.