If you want to keep a whole bottle chilled, you probably want a small cooler or insulated lunch bag, possibly with one or more reusable ice packs depending on how long you want to keep it cold. There are probably a million designs to choose from, but looking for a 2.0-bottle-sized case would narrow things down considerably. I don’t think I’ve used one since high school, unfortunately.
If you will definitely be drinking it, you could pour it in a vacuum flask of the appropriate size, ideally one with a drinking spout. The only drinking model I have experience with is this one:
It’s 24 fl oz, so much larger than you would need. I mostly use mine for water. There are approximately a million designs to choose from in a more appropriate size. Here’s a 16 fl oz size (one bottle of Soylent 2.0 is about 14 fl oz, which would leave room for ice if you desire):
I have no particular brand loyalty to Thermos, but the one I have still works great after two years. It’s actually advertised to keep things cold for 24 hours, but in my experience it’s more like 36-48 hours. So that’s something.