How big is the duck pond? Are you sure it's not azola, a tiny-leaf pond plant that turns red when it gets hot. I like azola because it composts really well and fixes nitrogen. But you don't want to leave it on the pond because when there are high levels of nitrogen in the water, you'll get it covered with algae, and then you've got a real mess.
I have a pool scooper on a long handle that I scoop unwanted stuff out of the pond with, so you could start with that. I
compost plants I scoop out.
It's probably going to take a few years for trees and pond plants to grow in it so the frogs will have cover, the birds will hang out in the trees and handle a lot of the issues. But levels of things, even pond plants, come and go from covering everything to not being there at all. Birds bring in plants and insects on their feet that will keep you busy every summer!
Mediterranean climate, hugel trenches, fabulous clay soil high in nutrients, self-watering containers with hugel layers, keyhole composting with low hugel raised beds, thick Back to Eden Wood chips mulch (distinguished from Bark chips), using as many native plants as possible....all drought tolerant.