OT: What kind of plastic is this?

Not enough information here. Do you have an IR spectrum of it?

It could just be polythene with an unholy amount of plasticiser in it.

The modern starch substitutes for plastic bags are starting to make an appearance on periodical magazines now but few are clear. The clear grade is OK for envelope windows but is somewhat more brittle.

Often there is a code on the plastic for correct recycling

No.

It's very soft, not at all brittle, and crumples and folds very easily.

No code. It's a simple clear general purpose bag.

Carefully burn a small piece. If it smells similar to candle wax its polypropylene.

Oops - should be polyethylene...

sorry

My guess(tm) is that the PE (polyethylene or polythene) has been doped with something to make it more biodegradable: The additive creates voids or caves in the PE which make it look like a sponge under a sufficiently powerful microscope. The microbes that can eat plastic live in the caves, thus accelerating decomposition. The addition of these caves slightly weakens the plastic, which is usually made slightly thicker to compensate. The plastic also tears more easily and has a rather "soft" feel instead of the usual PE smooth slick finish. Such bags often have some kind of identifying mark or advertisement indicating that it's more biodegradable, which makes me wonder if this is a correct guess(tm). Since the doping level is only about 1% of the plastic volume, detecting the density difference between regular PE bags and doped PE bags might prove tricky. Throw the bag into a working compost heap. If it falls apart and disappears in a few years, it's biodegradable PE.

Careful on the smell test. Plastic outgassing tends to be carcinogenic like the vaporized PVC on overheated wires during 3 Mile island long ago.

Why so much interest in this? We also see the crinkly grey bags used here for groceries but I prefer the brown soft as silicone plastic bags that are silent when crunched up for doggy poop bags.

Try putting a piece in a small jar with some biological detergent. If it is a biopol or modified starch that will dissolve it in just a few days. True olefin polymers will just sit there untouched.

Almost all magazines in the UK that arrive by post use the biodegradable starch based polymer for their outer mailing envelope now. It is thin and soft and waterproof for a couple of days in transit at most.