While it sounds obvious, you need to find exactly where the leak originated. Water will can migrate and start dripping far away from its source.

Curious that the leak started during a heavy rain. Look carefully around the existing drain(s). It is plugged or slow draining? Did rain splash up on a wall above the flashing and ingress there? Caulking/deck coating drying out, hardening, cracks? Could it be a clogged rain gutter above the deck allowing water to run down a wall making it appear that the deck is the leaking?

Check under the exterior door/glass slider. If it was raining hard and the deck was pooling, water may backup and get under the door threshold. Rain splashing could get under that threshold as well. Inspect the bottom of the door frame or around the slider track for leaks.

Can’t point you to a contractor, but someone with commercial flat roof experience is the ticket. Beware of anyone who says dumping a bucket of ‘special silicone sealant’ will fix it.