Revert "core/execute: set HOME, USER also for root users"

This reverts commit 8b89628.

This broke systemd#5246

Author: poettering

man/systemd.exec.xml

@@ -1705,7 +1705,9 @@
         <term><varname>$SHELL</varname></term>
 
         <listitem><para>User name (twice), home directory, and the
-        login shell. See
+        login shell. The variables are set for the units that have
+        <varname>User=</varname> set, which includes user
+        <command>systemd</command> instances. See
         <citerefentry project='die-net'><refentrytitle>passwd</refentrytitle><manvolnum>5</manvolnum></citerefentry>.
         </para></listitem>
       </varlistentry>

src/core/execute.c

@@ -815,10 +815,13 @@ static int get_fixed_user(const ExecContext *c, const char **user,
 
         assert(c);
 
+        if (!c->user)
+                return 0;
+
         /* Note that we don't set $HOME or $SHELL if they are not particularly enlightening anyway
          * (i.e. are "/" or "/bin/nologin"). */
 
-        name = c->user ?: "root";
+        name = c->user;
         r = get_user_creds_clean(&name, uid, gid, home, shell);
         if (r < 0)
                 return r;