Yes, the tank is polyethelene (PE). You won't find anything that bonds
well to PE. It is one of several commonly used low surface energy (LSE) polymers. LSE in practice means that the chemical makeup of the materials doesn't allow adhesives wet out when applied to them. Others LSE polymers include TPO, polypropylene, polyvinyl fluoride (aka Tedlar), and everyone's favorite PTFE (aka Teflon). PE is great for something like a water tank because stuff doesn't stick to the inside of it. But not so good when you want to attach something to it.
It is possible though to adhere things to PE and other LSE's if a proper surface treatment is applied first and you're not expecting to form a really strong mechanical bond (like say if you try to glue two sticks of plastic together and bend the joint).
In the case of foaming a PE tank the bond doesn't need to be really strong but you need some bond strength. So some surface treatment is in order. There are two options I know of: flame treatment and primers.
I fixed a couple cracks in my PE Hobie kayak by stop drilling the craks, then flame treating the crack surfaces then using West Systems gflex epoxy. I got very good adhesion, that was 2 years ago and the cracks have not reopened.
In my former work in solar module design and manufacturing we used Tedlar (PVF) as the backsheet material. Tedlar is also the stuff you see on the interior walls of commercial aircraft, because its easy to keep clean. We bought our Tedlar flame treated on one side and got great adhesion when we laminated the modules, good enough to last 30-40 years outside. If the maunfacturing folks screwed up and used the non flame treated side the Tedlar backsheets would peel right off by hand.
So I'm a big fan of flame treatment. You are not looking to melt the surface, just dull the shiny finish. You can also check whether its done the job by seeing if water sheets out on the flame treated surface significantly better than the non flame treated side. That is a sign that you've activated the PE surface and you'll get decent adhesion. For sure though try a small area first to be sure you're getting adhesion to the foam before going to the trouble of flame treating and spraying the whole tank.
Here is a 3M article explaining all this in more detail. Of course, they are trying to sell you on their primers, which is fine, you can look into that too, but also take a look at the graph showing improvement from simple surface flame treatment.