Simplify example Shiny app

[wlandau]

Prework

• [x] I understand and agree to the Contributor Code of Conduct.
• [x] I have already submitted a discussion topic or issue to discuss my idea with the maintainer.

Related GitHub issues and pull requests

• Ref: #157

Summary

Uses Shiny extended tasks and crew promises to simplify the example app in the vignette.

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 100.00%. Comparing base (c572f22) to head (3401506).

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Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #161 +/- ## ========================================= Coverage 100.00% 100.00% ========================================= Files 28 28 Lines 2000 2000 ========================================= Hits 2000 2000 ```

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