It’s possible! There’s a yearly bike race from Europe to China called The Sun Trip, where people mod their bikes with solar and batteries and ride 12k km to China.

You might like this documentary that covered the first Sun Trip that happened in 2018: https://youtu.be/P1LB0jPh7QQ

You nailed it: there is a conflict between surface area (wanting more for solar charging) and efficiency (you want it to be aerodynamic and light, hence less area for solar charging).

I also think an extendable canopy (for a car, not a bike) should be a better approach. I wonder if anyone tried it.