“Rollable” solar panels are still pretty stiff. You would need a beefier mechanism to handle the extra forces required. They also have a pretty significant “minimum turn radius” so they would need an entirely new design for their mechanism to work without damaging the panels.

They do make personal solar array with a surface area comparable to your umbrella idea, but those would take days to charge a cellphone, so the char you get walking around for a few hours is negligible.

It’s a cool idea, and would be a fun project to build and show off, but it’s not going to be marketable or practical without a whole lot of development in solar, battery and umbrella tech.