analysis_server: Refactor disk reads for examples directory

Fixes https://github.com/dart-lang/sdk/issues/50542

One primary principle is keeping the cost for _most code_
extremely low. Most code does not have an `examples/api`
directory. Most comments do not have `{@tool`.

Looking for directories on disk is expensive. Walking tokens
in comment text is cheap. So we can pay the price of walking all comments, prowling for `{@tool` text which we won't likely find,
and skip the work of looking for `examples/api` in _all_ parent
directories, until we find a comment with `{@tool`.

Don't check if `$parent/examples` exists before checking if `$parent/examples/api` exists. We don't care if `$parent/examples`
exists.

Don't create an `AanlyzerConverter` instance for _every element_
in a compilation unit while we are editing it. Instead, refactor
some of the `AnalyzerConverter` methods to be extension methods.

Change-Id: I812a1a435ee075e921782c1a57e9ed77325f9387
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/271863
Reviewed-by: Konstantin Shcheglov <scheglov@google.com>
Reviewed-by: Brian Wilkerson <brianwilkerson@google.com>
Commit-Queue: Samuel Rawlins <srawlins@google.com>