Add support for multi-window dialogs on Windows

[hbatagelo]

Design doc: https://docs.google.com/document/d/1eQG-IS7r4_S9_h50MY_hSGwUVtgSTRSLzu7MLzPNd2Y/edit?tab=t.0

This PR is a part of a group of PRs. Going from first to last, these must be merged in the following order:

• Add support for multiple top-level windows on Windows #56090
• Add support for multi-window popups on Windows #56092
• Add support for multi-window dialogs on Windows #56093
• Add support for multi-window satellites on Windows #56094

See also the corresponding framework PRs for multi-win support, starting from: flutter/flutter#157515

What's New

This pull request adds support for multi-window dialogs in the Windows embedder.

A new method is available in the flutter/windowing channel:

• createDialog(Map)
Map must contain the following key-value pairs:

  Key (String)	Value
  "parent"	The ID of the parent view (int), or null if the dialog doesn't have a parent
  "size"	The width and height of the dialog's client rectangle, in logical coordinates (List<int>)

  On success, a Map is returned with the following key-value pairs:

  Key (String)	Value
  "viewId"	The view ID of the window (int)
  "archetype"	WindowArchetype::dialog
  "size"	The current size of the window (width, height), in logical coordinates (List<int>)
  "parentViewId"	The view ID of the parent window (int), or null for a parentless dialog

  If the method fails, a PlatformException is thrown.

Pre-launch Checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I read the Tree Hygiene wiki page, which explains my responsibilities.
• I read and followed the Flutter Style Guide and the C++, Objective-C, Java style guides.
• I listed at least one issue that this PR fixes in the description above.
• I added new tests to check the change I am making or feature I am adding, or the PR is test-exempt. See testing the engine for instructions on writing and running engine tests.
• I updated/added relevant documentation (doc comments with ///).
• I signed the CLA.
• All existing and new tests are passing.

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

[flutter-dashboard]

This pull request executed golden file tests, but it has not been updated in a while (20+ days). Test results from Gold expire after as many days, so this pull request will need to be updated with a fresh commit in order to get results from Gold.

[jtmcdole]

Monorepo Migration Completed

TL;DR: Please migrate your PR to flutter/flutter

The flutter/engine repository has been migrated to the flutter/flutter repository. This PR will no longer be landed here and must be migrated. To migrate your PR to the flutter repository, please follow these steps:

1. Create a patch for this PR:

   • Generate a patch set that represents the changes in this PR. The exact method will vary depending on your PR's history. If your PR includes merges, it is highly recommended that you rebase it onto main first.

   git format-patch $START_COMMIT..$END_COMMIT --stdout > combined_patch.patch

2. Update the patch for the new engine location:

   • The engine source code now resides in the engine/ subdirectory within the flutter/flutter repository. You'll need to update the file paths in your patch accordingly.

   # Insert the `engine/` prefix to all paths. Note that this usage works on macOS and
   # linux versions of sed.
   sed -i.bak \
   -e 's|^\(diff --git a/\)\(.*\) b/\(.*\)|\1engine/\2 b/engine/src/flutter/\3|' \
   -e 's|^\(--- a/\)\(.*\)|\1engine/src/flutter/\2|' \
   -e 's|^\(\+\+\+ b/\)\(.*\)|\1engine/src/flutter/\2|' \
   combined_patch.patch

3. Checkout and set up your Flutter development environment:

   • Follow the instructions in Setting up the Framework development environment to check out the flutter/flutter repository.
   • Remember to rename the origin remote to upstream (e.g., git remote rename origin upstream).

4. Set up the engine development environment within the monorepo:

   • Follow the updated instructions in Setting up the engine environment, paying close attention to the changes in gclient setup and location.

5. Apply the patch to a new branch:

   • Create a new branch in your flutter/flutter repository.
   • Apply the updated patch to this branch:

   git apply combined_patch.patch

6. Open a new PR:

   • Open a new PR in the flutter/flutter repository with your changes.
   • Reference this original PR in the new PR's description using flutter/engine#<PR_NUMBER>.

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