No paint will make a significant difference, the film thickness is too thin.
How much space could you afford to give to insulation?
The most effective insulation material commonly available locally are the PIR or PU boards. Brands found in Wickes, B&Q etc are Celotex and Kingspan but usually 1 or 2 inches thick. The surface is not very hard so benefits from a bit of impact protection with any thin tough lining, thin ply, plastic wall lining etc.
Coachbuilt motorhomes commonly have 30 to 40 m thick walls the core of which is a PIR or PU foam.
You are probably hoping for something thinner. The Aldi aluminium foil faced bubble wrap is good value, 2/3rds of the price of Thermawrap and very likely came from the same factory. It really only works well if you can space it off the van wall or form an air space over the inner face. It is principally a barrier to radiant heat two cavities, an air gap on both sides, gives the best insulation. Without a cavity it is not much better than ordinary bubble wrap.
The black foam rubber sheet with a self adhesive layer, found via the internet, is available in various thicknesses. I had some 5 and 10 mm thick. It is fairly robust, impact resistant, but can be scratched or picked away. It isn’t a really good insulant but 10mm feels warmer to the touch. Not beautiful to look at!
I have not tried lining over that with stretch carpet but it might be worth a try. The sellers of the foam or carpet can probably advise whether it will stay stuck in place long term.
Stretch carpet alone is not a very good insulant but anything of this sort can make a difference to the feel of a freezing cold metal panel. Insulation follows the law of diminishing returns so even a thin layer of insulation will reduce heat loss through metal and glass areas but not enough to significantly lower the total energy needed to keep a van warm.
Don’t be tempted to conceal the edges of carpet or similar porous material behind the door seal. You run the risk of wicking damp into the interior.
Hope that might be some help.