I don't have the forest app connected to anything. I just use it in the background to make sure I take breaks. For tracking time I sometimes just use the timer functionality of the Beeminder app.
But thanks to your article I have also started to use toggl like you do. And then I have simply connected Beeminder with toggl using the official Beeminder integration.
Beeminder has over a dozen official integrations and then there are countless other ways to connect it with 3rd party apps using IFTT, Integromat, Zapier, Tasker, etc.
For a list of ways that allow you to integrate Beeminder with other apps check out these two links:
https://forum.beeminder.com/t/beeminder-integrations-megalist/5091
https://help.beeminder.com/category/10-integrations?sort=name