I have a lot of irises I grow as marginal plants in my pond. I have Siberian irises, Japanese irises, a Louisiana Iris and an Iris versicolor. Do you know what kind your water iris is, since a lot of different species could fall under that name? If not it doesn’t matter, all mine grow about the same and I treat them all alike, they just look a bit different.
Since I put my pots in a pond I may do things a bit differently but when I plant mine I make a soil sandwich (mmmm munchies…) using gravel, kitty litter and boring old dirt. I put a layer of gravel on the bottom of the pot to keep smaller particle things from leaking out. Then add on top a layer of cheapo, non-scented, dollar-store kitty litter because when it is wet it becomes clay and holds moisture well plus keeps the soil added later from leaking out too. Then add some dirt. I usually use whatever crappy, low nutrient, dirt I dig up in the yard because I don’t want to add a lot of nutrients to the water with the soil and possibly get more algae. I plant the roots in this layer and then top off the dirt with a little bit of kitty litter again and then cover it all with gravel on the top of the pot. Then I run a bit of water through it to get some of the dust from the gravel and kitty litter out and then sit it in the water wherever I want and *try* to get the top of the pot and the plant’s crown level near the surface of the water…but usually it is submerged a bit and is fine.
Depending on your particular Iris, the sphagnum and peat may be unnecessary but I think there may be some iris which prefer acidic marshes/bogs and I doubt it would hurt the other irises anyways since some people use those materials with their standard potting soil mixes too.