Problems with user systemd unit

Basically I want to use ssh-agent and tried to implement starting the ssh-agent as described (SSH keys - ArchWiki).

After login, when I issue the command systemctl --user status ssh-agent.service I receive the following output:

● ssh-agent.service - SSH key agent
      Loaded: loaded (/home/andres/.config/systemd/user/ssh-agent.service; enabled; vendor preset: enabled)
      Active: failed (Result: exit-code) since Fri 2021-04-30 06:05:40 CEST; 2min 18s ago
    Process: 3950 ExecStart=/usr/bin/ssh-agent -D -a $SSH_AUTH_SOCK (code=exited, status=2)
      Main PID: 3950 (code=exited, status=2)

Apr 30 06:02:06 chani systemd[567]: Started SSH key agent.
Apr 30 06:02:06 chani ssh-agent[3950]: SSH_AUTH_SOCK=/run/user/1000/ssh-agent.socket; export SSH_AUTH_SOCK;
Apr 30 06:02:06 chani ssh-agent[3950]: echo Agent pid 3950;
Apr 30 06:05:40 chani systemd[567]: ssh-agent.service: Main process exited, code=exited, status=2/INVALIDARGUMENT
Apr 30 06:05:40 chani systemd[567]: ssh-agent.service: Failed with result 'exit-code'.``

While when issuing systemctl --user start ssh-agent.service after login the output changes to:

● ssh-agent.service - SSH key agent
     Loaded: loaded (/home/andres/.config/systemd/user/ssh-agent.service; enabled; vendor preset: enabled)
     Active: active (running) since Fri 2021-04-30 06:10:06 CEST; 4s ago
   Main PID: 8958 (ssh-agent)
     CGroup: /user.slice/user-1000.slice/user@1000.service/app.slice/ssh-agent.service
             └─8958 /usr/bin/ssh-agent -D -a /run/user/1000/ssh-agent.socket

Apr 30 06:10:06 chani systemd[567]: Started SSH key agent.
Apr 30 06:10:06 chani ssh-agent[8958]: SSH_AUTH_SOCK=/run/user/1000/ssh-agent.socket; export SSH_AUTH_SOCK;
Apr 30 06:10:06 chani ssh-agent[8958]: echo Agent pid 8958;

I assume, that as I defined SSH_AUTH_SOCKET in my profile it is now picking up the env variable from there, but shouldn´t the “Environment=SSH_AUTH_SOCK=%t/ssh-agent.socket” entry in the unit do the trick?