In lieu of a URL scheme for the Beeminder app, I was able to create an iOS Shortcut to call the Beeminder API directly:
https://www.icloud.com/shortcuts/b03d66193a89440da7af6d22133695f3
It’s less convenient than delegating the API call to the iOS app would be, but this has made it easy for me to make a whole bunch of other shortcuts for quick entry of my manual data points.
This shortcut is intended to be called with the “Run Shortcut” action rather than run on its own. I’ve been building goal-specific shortcuts with some interactive prompts for composing the datapoint and comment, then passing those values into this “Create Beeminder Data Point” shortcut.