Private Keys – How do three addresses of the same (un)compressed key work?

How does it actually work?

I think the easiest way forward is to hold fast to the truth that addresses are fictitious. This is sometimes a convenient way to reference a locking script. Focusing too much on addresses takes us away from the fundamental truth.

I hope things will become clearer if you think of script locks instead of addresses.

From a pair of private and public keys, there are various ways to construct different types of lock scripts that can use the public key to unlock using the private key. There are several standard locking scripts where public keys are used.

The owner of a key pair can separately track transactions that contain a specific but unique type of locking script with the same primary key.

I believe blockchain explorers mostly index with a summary of the locking script. Therefore, we create a separate transaction list for each unique locking script.

Every transaction list (different address types) is different. How can this be if the private keys are the same?

The truth is that the transaction does not pay for a specific private key, but rather whoever can unlock the locking script. Sometimes the unlock may involve no private key, and sometimes it may involve multiple private keys.

Additionally, some types of locking scripts reveal your public key, while some do not. Therefore, Explorer cannot know whether the output of some types of transactions contain the same key pair. Therefore, the explorer cannot reliably group transaction outputs by a common private key.