Would it make sense to think of Bitcoin as a money or value protocol in a similar way to other protocols for data (TCP/IP), STMP, POP3, etc?
I think yes. It's just another communication protocol, but with the difference that there's value exchanged via cryptographic means. There are actually lots of Bitcoin protocols, such as the Bitcoin blockchain full nodes, the light client servers (SPVs), the lightning node, the block explorers etc. But the main layer is one protocol, just like TCP/IP, yes.
With Bitcoin as the money protocol, I think the size of the value transferrable is dependent on the size (value) of BTC relative to e.g. USD. In other words, the usability of the protocol improves as the amount of value that can be transferred over the protocol increases.
Ι don't understand how that's true. Was bitcoin more usable in 2021, valuated at $60k? Or, was it about the same usable in December 2017? Nah. The usability of the protocol improves overtime, but not accordingly to the amount of value that is inside the system.