Remove demo build script (#4439)

### What

Closes #4428
Closes #4277

### Checklist
* [x] I have read and agree to [Contributor
Guide](https://github.com/rerun-io/rerun/blob/main/CONTRIBUTING.md) and
the [Code of
Conduct](https://github.com/rerun-io/rerun/blob/main/CODE_OF_CONDUCT.md)
* [x] I've included a screenshot or gif (if applicable)
* [x] I have tested the web demo (if applicable):
  * Full build: [app.rerun.io](https://app.rerun.io/pr/4439/index.html)
* Partial build:
[app.rerun.io](https://app.rerun.io/pr/4439/index.html?manifest_url=https://app.rerun.io/version/nightly/examples_manifest.json)
- Useful for quick testing when changes do not affect examples in any
way
* [x] The PR title and labels are set such as to maximize their
usefulness for the next release's CHANGELOG

- [PR Build Summary](https://build.rerun.io/pr/4439)
- [Docs
preview](https://rerun.io/preview/349f458a791f8e1b6d58fe6e182b06824e7470eb/docs)
<!--DOCS-PREVIEW-->
- [Examples
preview](https://rerun.io/preview/349f458a791f8e1b6d58fe6e182b06824e7470eb/examples)
<!--EXAMPLES-PREVIEW-->
- [Recent benchmark results](https://build.rerun.io/graphs/crates.html)
- [Wasm size tracking](https://build.rerun.io/graphs/sizes.html)

.gitignore

@@ -44,9 +44,6 @@ perf.data*
 # Screenshots from samples etc.
 screenshot*.png
 
-# Web demo app build
-web_demo
-
 # Saved example `.rrd` files
 example_data