How to repair puncture hole in my NEW down coat?

This is the first time I’ve ever had a hole in the outer shell of one. It’s in an area that will get a lot of wear, so fixing it as soon as I can is important. The coat falls to the top of the thigh, and the 3/8” (or 4 mm) hole is at the back, right where it will hit the back of a seat. It’s already run a little bit.

The shell is 66% nylon and 34 % polyester. Fill is part down and part polyester fiberfill. What I see coming out of this hole is fiberfill. I can’t tell from the tag where the down is located. It says “down bag” – whatever a down bag is - is 100% duck down and feathers.

Even with the tiniest hand stitches, the repair will be visible. Hopefully I can minimize it. And stop it from running further. (And wouldn't you know it, I just got a custom hat and scarf crocheted by a local crafter to match it. I have a huge head so can't wear commercial hats. I’ve tried making them, then didn’t like them)

Please tell me what might be the best way to fix this.

Fray check first?
Fine fusible interfacing? Work a small circle through the hole, then iron very carefully with the tip to secure it ?

Follow each with small stitches?

PLEASE help me fix this! Thanks very much for any help you can offer.