My last first aid course didn't mention tampons specifically, but if you need to stop heavy bleeding, anything is on the table.

We were told that the general practice with a major wound was essentially to use a rolled up bandage to wipe the worst of the blood away so you can see where it's coming from, then put said bandage over the probable artery and apply lots of pressure.

Your job as first aid is to keep someone alive until paramedics arrive. Tissue damage from a tampon gluing itself in can be fixed. Total blood loss less so.

They did say they're an option for a major nosebleed though.

Abstract lists tampons as one of the things it would teach how to use in an emergency

There are situations where you need to pack a gsw with gauze but a tampon is a terrible thing to use for that and you’d be better off using a tshirt or something.

https://youtu.be/soiku6XyXvQ?si=dJMXjqyttJqsHoJM

FWIW I've seen little single use packs of blood clotting powder in the camping section at both Target and Walmart recently (in the last few months) probably worth grabbing a few first aid kits.