Is there a Homey Bridge app that is able to use expected rain as a trigger?

For sunshades though, I think the best solution is a rain sensor.
Weather services are not the most precise tools.

There’s very cheap DYI (just two wires) ones, like Aqara flood sensor (Homey Bridge supported), connected to a special circuit board, which closes the circuit as soon as water drops appear:

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Ready to go, but 3 to 4 times more expensive, and bridge supported:
Popp rain meter: POPP Z-RAIN (700168)