They mention stdio specifically under the transport section of the spec.

Most protocols are transport agnostic, but http APIs tend to require HTTP methods. Http itself is transport agnostic, but truthfully all we’re doing is shuffling bytes around.

If you look at the stateless examples in that PR, they both assume some state (specifically the capabilities) and just behave accordingly.

To get the full features of the protocol (like notifications) a stateful connection would still be required.