The main outer shell looks like it's recyclable plastic, but then inside that it (from 1:18 onwards) looks like heavy-duty Styrofoam / "Extruded polystyrene foam" which I know my local council won't take.

Styrofoam is terrible stuff - bulky but not heavy (it's 98% air), not recyclable, and fragile enough that it's almost guaranteed to break down into fragments and small beads which are light enough to be dispersed by a breeze. Microplastics to go.