Adding the demo app from my I/O talk. Because AI.
## Pre-launch Checklist
- [x] I read the [Flutter Style Guide] _recently_, and have followed its
advice.
- [x] I signed the [CLA].
- [x] I read the [Contributors Guide].
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] All existing and new tests are passing.
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Co-authored-by: Brett Morgan <brett.morgan@gmail.com>
