Why does `ps -e` display information about the current user's processes?
The “e” or -e option was originally for every process.  It was deprecated with the -A for All processes.  It remains as a carry over for POSIX compliance with historical versions.
The difference between -a and -A is

-a only shows other users processes with a controlling terminal.
-A shows all process even if they are not attached to a terminal, like a daemon

According to the man page,

The ps utility supports the Version 3 of the Single UNIX Specification (``SUSv3'') standard.

macOS is one of the few certified POSIX compliant Unix operating systems that conform to the Single Unix Specification as such, all utilities included must also be POSIX compliant.
Additionally, in the man page, there is a section titled Legacy Description (IMO, bad wording) where it details the difference between POSIX ps and Legacy ps

In legacy mode, ps functions as described above, with the following differences:
-e      Display the environment as well. Same as -E.