You should be able to do this through your Apple account. There’s a manage subscriptions page on your account in Apple and you just select Zwift and cancel it.
As far as I am aware pausing and cancelling are effectively the same. The only difference seems to be that with pausing Zwift will automatically start charging you again after the pause period (which is only 2 to 8 weeks, any longer than that and you have to cancel your sub). With Apple you should be able to restart your subscription when you want to resume Zwifting.
I think the pause option is not available due to the way Apple works. Only the user has control over the Apple payments, 3rd parties like Zwift do not have the authority to stop or start Apple payments.