Can you give a linky for treated battens you have in mind?
No it was only if the studwork was going to be against an existing solid wall that something like 2×1 battens might have been suitable.
2×2 will be too flimsy though?
You would get away with it as it will only be 1.4M high but I would definitely go for 3X2, More solid and stable and imo easier to work with.
As for regularised v ordinary sawn I would select the timber myself and just go for whatever is straighter, IME CLS/regularised timber can be bent and twisted to appalling degrees, whilst ordinary sawn timber can be extremely straight. It just depends and you can’t really be sure until you see it.
Obviously 3X2 ie 75X50 sawn will be a tad chunkier than 70X45 regularised.
Sawn timber is also likely to be far wetter than CLS/regularised which should be bone dry. That might be an issue if you are cutting by hand rather than cutting using an electric chop/mitre saw. Obviously you will see when you select it.