His method already does that. Creating a target for a single service is very much overkill. Though creating a target like setup or pre-default and putting in there might be a fine idea if you have other services you want to run that way.
But, since the unit is already setting a fixed path for the agent, I would just put that path in my .profile and call it a day. Having systems do environment variable injection seems too fragile to me, especially for static variables.
https://git.sr.ht/~whynothugo/dotfiles/tree/c0bf9296c6ca8661...
Note that the ordering is important so that `SSH_AUTH_SOCK` is passed down to other services.