the default systemd service will run caddy as the caddy user i think

otherwise you can choose any user to run a systemd system service

Create a user, and then a systemd unit for it, under ~/.config/systemd/user/ with contents like these:

[Unit]
Description=Caddy web server
After=network.target

[Service]
ExecStart=/usr/local/bin/caddy run --config /path/to/Caddyfile --envfile /path/to/Envfile
ExecReload=/usr/local/bin/caddy reload --config /path/to/Caddyfile --envfile /path/to/Envfile
Restart=on-failure
User=caddy
Group=caddy

[Install]
WantedBy=default.target

Adjust the paths in the arguments. It will require systemctl daemon-reload for such unit to be available for enabling and starting it…