hbomax doesn't see my apple subscription, how long does it take for hbo to be notified?

If you subscribed through Apple, you will first need to verify your existing subscription with HBO separately, in order to watch it in a browser (and not through the HBO app on an Apple device).

https://help.hbomax.com/

If HBO doesn’t offer any options to acknowledge your subscription through Apple, and you can’t sign in with your Apple ID account, then you can’t watch it in a browser.

You may want to consider switching to an HBO subscription through HBO directly, to be more independent of devices, and if viewing in a browser is important to you.

On what device are you trying to watch HBO Max?

HBO Max doesn't have a separate to "verify" the subscription. They send me back to my Apple device. My account is active according to Apple and charges every month.