just a few rocks should do the trick ? What about putting the 'root ball' of
the plants inside a plastic bag or something like that ? I don't want the
water crystal clear but right now we cannot even see the fish.

Put rocks on top of the dirt, that will keep most of it in, as well as
keeping the carp out. Carp love to dig in the dirt. A lot of the
dirt will settle out over time. If you have living things in the
water, it won't be crystal clear, you will have algae blooms, plant
debris, all sort of things. Part of the world of ponds.