How do I identify the number of unique transaction addresses using an application/protocol on Ethereum?

The best way to identify the number of unique addresses using the protocol would be to access the Etherscan analytics tab. Here you can find a daily rundown of individual senders and receivers. Another method would be to create an app yourself or find a block explorer.

You will typically need to have a node and get the Blockchain data (AKA blocks.) Then you’ll need to know the address of the smart contract that you’d like to observe. After this, if you know the ABI, you can either look at the events fired by the contact or look block by block at the transactions calling the contract and saving the caller address.

Having a database to store this information would also be helpful if these interactions need to be reviewed for data analysis later down the line.