You are right it is a like a local table to the connection.
According to the link you have under the subheading Temporary Tables, it says:
A TEMPORARY table is visible only within the current session, and is dropped automatically when the session is closed
Simply put, once the DB Connection terminates (normally or abnormally), the table disappears.
This just looks like a quirk with the optimisation of that query producing a slightly different tree shape when simple parameterisation is attempted vs when it isn't.
This is not attempted in the case of the local temp table but is for the global temp table and permanent table.
The auto parameterisation does not succeed in any case but when attempted on this ...