It happens and it’s not a big deal. Especially if you won’t destroy the removed inserts. For next time… put the plate with the insert on a Vice (as is in your picture). Tighten the Vice as much as needed for the insert not to turn while unscrewing it. Chances are that it unscrews without destroying it. Run a 8/32 tap through it and put it back in the ski. If the ski brand is what I’m assuming it is, most of the times you can put it back without using any adhesive (better use some).
also Helicoil is a thread repair insert, not an insert by itself. Unless they now sell inserts too.
I would write to the ski company to sell me some inserts so my ski would look as it was before.
if your insert pocket is not widened. Use the same inserts. Your ski brand, usually does not need oversized ones.
D3 sell inserts but they will not look the same as yours. They also sell oversized ones.
if you need to buy from a local hardware store, look for 8/32” brass wood inserts.
No special tools needed to reinstall, just a screw and a nut. Just be careful with any excess adhesive that can go in the threads and dries there. If you use any adhesive, mask everything around the insert hole with masking tape, if you want your ski to still look good.
ps. If you have an older model of the same brand you can use it as a donor. Until you receive some from the ski company. You can remove one with the screw and the nut in it. Same way as installing one.
good luck
Alex