Create an App example within the repo like the other SDKs

[marandaneto]

https://github.com/getsentry/sentry-dart/tree/main/flutter/example

[jennmueng]

I can pull in the sample app I made that I've been using to test it.

[github-actions[bot]]

This issue has gone three weeks without activity. In another week, I will close it.

But! If you comment or otherwise update it, I will reset the clock, and if you label it Status: Backlog or Status: In Progress, I will leave it alone ... forever!

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"A weed is but an unloved flower." ― Ella Wheeler Wilcox 🥀

[lucas-zimerman]

Relates to #261