I purchased membership on mobile. The payment went through. However it doesn't show that I have membership, I cannot log into membs world, and I cannot purchased additional membership as it seems to think I'm already a member.
Membership purchased through Google Play or Apple may take up to 24 hours to be added to your account. If you did buy it through either method and you are unable to enter a members world, you should wait a few as it should automatically update on its own.
In any case, here's the Support article pertaining to your concern:
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Membership / Item not added to account
• When you make a purchase through Google Play / Apple it can take up to 24 hours for the membership to be added to your account.
• If you've purchased membership via Google Play / Apple but are unable to log into a members world, hold tight your membership should be added shortly.
• If you've waited more than 72 hours, check your other accounts (including Game Center) to make sure you didn't purchase your membership on the wrong account by mistake.
• If your Google Play payment was definitely successful, visit the in-game store and you should receive a prompt to pick up your purchase. Make sure you're logged into the same Google Play account that you made the purchase on.