No experience of this particular model, as it seems fairly new, but it’s on my ‘radar’.
Yes, it appears that the plastic insert is the plunger, but from my experience with their smaller adventure pot (with the two small plastic cups), it should be BPA free. Don’t know if that will affect the taste once you add boiling water.
Their smaller (470 ml) coffee press/ flask is still available, albeit at a pricier £28 approx.
It got me excited (as you can tell) because I had been thinking about buying a robust French-press and you can also use this to boil your pasta or whatever.
My only reservation would be about replacing the mesh filter should it wear out.