How to purchase an app outside of Family sharing

I am guessing what you mean is you want to pay for it yourself instead of having it charged to the organizer's payment method. To do that, make sure you have enough personal account balance so it is charged to that first. Read the document for the link to "learn how purchases are billed if a family member has Apple ID balance" ( How apps, content, and subscriptions from Apple are billed - Apple Support ).

If you're in a Family Sharing group then any purchase is still made by you personally but is available to others in the group unless you hide the item. Hide purchases from the App Store - Apple Support