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If you bought something online with a debit or credit card and did NOT log into your Paypal account then of course it won't show on that Paypal account because you bought as a 'guest buyer'.
However your seller may have processed that payment using their Paypal 'card reader' and so Paypal would show on your bank or card statement.
If that is not the case then contact customer services AND your card issuer to query the transactions.
If you need to open a dispute for a 'guest buyer' transaction then you can.......
1. Phone Paypal customer services and see if they will open one for you OR
2. Contact your card issuer for a chargeback.