Yes, barley straw will definitely help control algae. You can even buy the extract in a bottle, and it’s safe for fish so probably safe for other wild life too. On the other hand, the wildlife that’s there (including the frog) has moved in to an environment that they are probably already happy with so I wouldn’t feel a need to change it too dramatically. Algae is usually only an aesthetic problem unless if gets too extreme.
In the long term, getting plants growing is the best action. They will begin to out-compete the algae and it will slowly disappear. Spring is always the prime time for algae growth, but as the light continues to grow into summer, the plants will thrive and the algae should reduce naturally.
I have a goldfish pond of about 1000 litres in our urban garden. We recently found we had frogs and it’s great to see them. The pond has a cat fence so the frogs are safe so long as they stay within the pond itself.