Description

Changes the interaction between the view controller and engine in both the C API and
the engine API, so that there's always an engine (as on other platforms) rather than
the engine APIs being specific to headless mode.

While adjusting the C API, this does a large cleanup:

• Renames all methods to follow a FlutterDesktop (prefix) + "class" name + method-style name.
  E.g., FlutterDestkopViewControllerCreate rather than FlutterDesktopCreateViewController.
  This makes it easier to see what functions operate on which conceptual "object" in the API.
• Reorders and groups them by the object they operate on.

Related Issues

Fixes flutter/flutter#61966

Tests

I added the following tests: Adjusted client wrapper tests for the changes.

Checklist

Before you create this PR confirm that it meets all requirements listed below by checking the relevant checkboxes ([x]). This will ensure a smooth and quick review process.

• I read the contributor guide and followed the process outlined there for submitting PRs.
• I signed the CLA.
• I read and followed the C++, Objective-C, Java style guides for the engine.
• I read the tree hygiene wiki page, which explains my responsibilities.
• I updated/added relevant documentation.
• All existing and new tests are passing.
• I am willing to follow-up on review comments in a timely manner.

Breaking Change

Did any tests fail when you ran them? Please read handling breaking changes.

• No, no existing tests failed, so this is not a breaking change.
• Yes, this is a breaking change. If not, delete the remainder of this section.
  • I wrote a design doc: https://flutter.dev/go/template Replace this with a link to your design doc's short link
  • I got input from the developer relations team, specifically from: Replace with the names of who gave advice
  • I wrote a migration guide: https://flutter.dev/go/breaking-changes-template Replace this with a link to a pull request that adds the migration guide to https://flutter.dev/docs/release/breaking-changes
  • Windows is not yet subject to the breaking change policy.

This is only a breaking change at the C API level, so is very unlikely to affect actual users since the template only uses the C++ wrapper.