Attaching video doorbell to stucco over rigid foam insulation
It would be important to find out if the entire column is rigid foam, or if it has a wood/steel/concrete/plastic core. If it has a core, you can use whatever type of fastener is ideal for that material (and long enough to penetrate the foam layer).
If it is truly rigid foam all the way through, you might consider drilling a hole and then using a molly fastener which when engaged would push hard outward from the hole against the rigid foam. Some kind of slow-drying glue or epoxy may help enhance that effect.
Otherwise, you're probably looking at some other kind of preparation. If you can engage a block of wood large enough (2x4 or 1x4) to mount the doorbell bracket, you may be able to embed it with glue and repair the stucco around it so it looks somewhat natural.