Yes, systemd has ability to run user services. For every logged in user there is one daemon socket that user can access to run services without ever rising privileges. They can run in background automatically as soon as you log in (at least one user session must be opened) or alternatively you can enable lingering for your account that assures it’s always up, so your user services can start on boot without you even logging in. It gets units from couple of directories - system packages can install user services in /usr/lib/systemd, custom global user services can go to /usr/local/lib/systemd for any individual user, theres also /etc/systemd and ~/.config/systemd for unit files of particular user.