Change the analytics instance that the generated api.flutter.dev and master-api.flutter.dev use.

part of https://github.com/flutter/flutter/issues/136500

this should not affect any production code, it merely runs the tests on CI and makes the changes needed to get them passing.

It looks like the logic added here:


https://github.com/flutter/flutter/pull/131951/files#diff-297ee4cfe6d9bffc2fa1376918a50b8e4165ada4569575880c40811b6f749265R18

got dropped in the refactor here:

https://github.com/flutter/flutter/pull/132710

## Description

This re-lands #132353 with some additional options for keeping around the staging directory, so that the recipe for publishing docs can give those options and have the staging directory left around for deploying to the website.

Reverted in #132613

## Related Issues
 - https://flutter-review.googlesource.com/c/recipes/+/49580

Reverts flutter/flutter#132353

Educated guess that this is causing the docs failures: https://logs.chromium.org/logs/flutter/buildbucket/cr-buildbucket/8772644466113801713/+/u/Docs/Deploy_docs/Firebase_deploy/stdout

## Description

This cleans up a lot of issues with the API doc generation.

Here are the main changes:
 - Rename `dartdoc.dart` to `create_api_docs.dart`
 - Move the bulk of the operations out of `dev/bots/docs.sh` into `create_api_docs.dart`.
 - Delete `dashing_postprocess.dart` and `java_and_objc.dart` and incorporate those operations into `create_api_docs.dart`.
 - Refactor the doc generation into more understandable classes
 - Bump the snippets tool version to 0.4.0 (the latest one)
 - Centralize the information gathering about the Flutter repo into the new `FlutterInformation` class.
 - Clean up the directory handling, and convert to using the `file` package for all file and directory paths.
 - Add an `--output` option to docs.sh that specifies the location of the output ZIP file containing the docs.
   - Defaults to placing the output in `dev/docs/api_docs.zip` (i.e. where the previous code generates the file).
 - Moved all document generation into a temporary folder that is removed once the documents are generated, to avoid VSCode and other IDEs trying to index the thousands of HTML and JS files in the docs output.
 - Updated pubspec dependencies.

## Tests
 - Added tests for doc generation.

Fixes https://github.com/flutter/flutter/issues/130978 

## Pre-launch Checklist

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there for submitting PRs.
- [x] I read the [Tree Hygiene] wiki page, which explains my
responsibilities.
- [x] I read and followed the [Flutter Style Guide], including [Features
we expect every widget to implement].
- [x] I signed the [CLA].
- [x] I listed at least one issue that this PR fixes in the description
above.
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] I added new tests to check the change I am making, or this PR is
[test-exempt].
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel
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* x

* docs

* add code to generate new icon demo and make font family optional

* remove trailing spaces

* Update update_icons_test.dart

* remove trailing space

use 'dart pub' instead of calling the pub executable directly

* Prevent double underscores after replacement

* add test

* remove trailing space

* Update update_icons.dart

* formatting

* more formatting

* simplify safety checks

* add safety checks tests

* formatting

* update copyright

* naming

* revert copyright

* add `fontFamily` option

* tweak diff messages

* Update update_icons.dart

* don't exit if platform adaptive icon not found

* remove trailing spaces

* remove warning and fix insert_chart (outlined) dartdoc

* x

* add error message when exiting due to failed safety checkes

* fix icon reference

* fix rewrite for onetwothree

* Migrate flutter conductor out of dev/tools and into its own directory

* flesh out documentation

* fix analysis options

* fix integration test

This reverts commit e86f9c7a.

This reverts commit 98a96189.

This reverts commit 0cbe5975.

This reverts commit 8b6baae4.

Our current top crasher is an unclear error when ProcessManager fails to resolve an executable path. To fix this, we'd like to being adjusting the process resolution logic and adding more instrumentation to track failures. In order to begin the process, the ProcessManager has been folded back into the flutter tool

This reverts commit b7f5aef1.