Your explanation assumes that scope and scale are part of the definition which it is not.
If you keep zooming in or zooming out the definition of E2E keeps changing under your statement.
If the only knowledge a system has is between a sender and a receiver (Which satisfies even your definition of “intended recipient”) then TLS is E2E encrypted.
E2E is about the sender encrypting, and only the intended receiver decrypting, with nothing in the middle able to read the data.
TLS is not designed for that, as the server you connect to is not necessarily the intended receiver, yet it can see everything.
With E2E, you can send data to a server, which is not the intended receiver, and it won’t be able to read it.
Your explanation assumes that scope and scale are part of the definition which it is not.
If you keep zooming in or zooming out the definition of E2E keeps changing under your statement.
If the only knowledge a system has is between a sender and a receiver (Which satisfies even your definition of “intended recipient”) then TLS is E2E encrypted.
The definition of E2EE has evolved since the concept surfaced. You seem to be stuck with the original meaning.
TLS does not fit the modern definition.