I would give it time before adding chemicals

Thank you for the advice. How much more time do you recommend?

I doubt that many here would suggest chemicals anyway. It would be useful to know where your pond is and how large and deep. I have never heard of anyone objecting to plant roots either. They are part of your biochemical and mechanical filtering system. To the extent that you have a problem, it is likely due to a mostly uncovered pond. Most ponds have At Least 50% coverage or some shade. It may be too late to change that this year.

It took 4 years for our new pond to balance.

We did use pond salt to help keep the algae down. It helped, but was harsh on the plants.

The best way to keep algae away is to use a UV filter. It kills the algae. We are in New England. We start up the UV filter in April.