But I believe the server itself is started in the interactive mode (if that's the right term for it) because immediately after those lines, you also see this
I didn't realize stand-alone was the same thing as single-user mode –– are you sure? I guess I don't know what the alternative is to "a stand-alone backend."
The server is started using a straightforward call to "postgres". It's not using the --single flag, which is what I assume is needed for the single-user mode.
No, single-user mode is a special case for recovering from mistakes:
The postgres command can also be called in single-user mode. The primary use for this mode is during bootstrapping by initdb. Sometimes it is used for debugging or disaster recovery; note that running a single-user server is not truly suitable for debugging the server, since no realistic interprocess communication and locking will happen. When invoked in single-user mode from the shell, the user can enter queries and the results will be printed to the screen, but in a form that is more useful for developers than end users. In the single-user mode, the session user will be set to the user with ID 1, and implicit superuser powers are granted to this user. This user does not actually have to exist, so the single-user mode can be used to manually recover from certain kinds of accidental damage to the system catalogs.
In the Gist I do not see a call to postgres by itself. I only see with --single.