Don't use example folder as a project type signal (#97157)

The code to generate platform files used to use the presence of an
'example' folder to determine whether or not a project was a plugin (in
which case that generation is bypassed). Later, robust detection was
added based on the pubspec.yaml `plugin` key, but the old check was left
in place. This creates false positives where people who add an example
folder to their app project start getting mysterious failures.

Since the pubspec check is definitive, there's no reason to continue to
use the presence of `example` as an indicator at all.

Fixes https://github.com/flutter/flutter/issues/87007