Ring Motion Sensor Triggers Timed ON event for for 3rd party smart light switch

We are looking for a way for a Ring motion sensor (and/or doorbell) to trigger a timed event (Turning on a light for XX seconds/minutes) for a NON-RING 110V light switch. There are 3 flood light fixtures on a circuit with an on/off switch. We were hoping to replace this on/off switch with a Brilliant brand or other light switch and trigger on/off of this lighting circuit and all 3 of its non-Ring lights by using a Ring motion-detection or the Ring doorbell. Any ideas how this could work? Ideally the motion sensor would not be battery-powered, but instead be hard-wired for longevity. Thank you.