Profile Launcher (ProfileLauncher.app | Loshadki Apps) covers what in my opinion is a glaring omission from Apple: the ability to unconditionally switch to a specific Safari Profile Window. Profile Launcher is a wrapper on Safari’s accesibility features so it has the capability to investigate the available profiles and creates, just that: the ability to switch to an existing profile if it exists or launch a new one. It can also provide specific “apps” that can easily be added to any app launcher or you can use its own protocol URL.
Highly recommended! (There are 1000 free activations, by the way).