An intriguing photo. Most water plants looks softer than that. I am certain it is not a milfoil. And it may not be an aquatic plant. Are you able to check it for flowers etc ?
I've ripped up a bit and added more photos. I may have misled everyone earlier by stating that leaves were 40mm when they are actually more like 10 mm (I was confused by another species also present.) Leaves and stems are quite soft. Almost certainly an aquatic plant - it is growing out to about 50cm inland from the shore and down to about 10cm under water.
nice update, I'm still intrigued. And a bit puzzled. hopefully it will flower soon Is there any way I could have a handful of the plant ? (i'd be happy to meet up at a place / time convenient for you). Water plants keep quite well in the fridge, for a couple of days, in a plastic or ziplock bag, and a bit of moisture.