I don't know Bluewallet, but maybe this can help you, maybe not. Maybe that depends on the mix of on-chain vs lightning network transactions you have been using.
I copy my public key (using the "receive" button of bluewallet to get said key)
I enter that address into block explorer type websites. It shows zero balance.
When you tap "receive" on your phone, if it cares for privacy, it should give you a different and unused address each time.
Is the address generated to receive coins not the right one to use for this purpose?
That address would be the right one to use for that purpose, not before it has been given to some other person or system. In case it is a new address each time you tap.
I don't know how to view any other
You look for some panel of balance history, and look for past transactions' addresses, those used addresses would be what you should feed chain explorers when reading past transactions.