Is the coat lined ? You could mend it through both layers or unstitch the lining and mend only the top layer. It is a tiny rip, but also a opportunity to practice adding a patch at the back of the fabric.
Satin stitch, fishbone stitch or buttonhole stitch could be an option to cover the repair. A little flower could also work, there are lot’s of video tutorials that explain it well !
Patch it ? You can sacrifice one pant to donate patch material to save the others.
I find doing it by hand is easiest, as wrestling the pants under the machine is tricky. If you want a less visible mend, you can put the patch behind the broken fabric, at the cost of durability.
Press on patches also exist and seems to work fine, I don’t have a lot of experience with it though.
One recommandation for patches in general, is to cover a much bigger area than the hole, otherwise you might have to redo it very soon.