Add a workflow for publishing flutter packages

[natebosch]

Closes #1259

Add a second copy of the publish workflow with use-flutter: true. Add ignore-packages to both workflows to ignore published packages for the non-relevant SDK.

[github-actions[bot]]

Package publishing

Package	Version	Status	Publish tag (post-merge)
package:http	1.2.3	ready to publish	http-v1.2.3
package:http_profile	0.1.0	already published at pub.dev
package:web_socket	0.1.6	already published at pub.dev

Documentation at https://github.com/dart-lang/ecosystem/wiki/Publishing-automation.

[brianquinlan]

Is this ready to land?

[github-actions[bot]]

PR Health

Breaking changes :heavy_check_mark:

Package	Change	Current Version	New Version	Needed Version	Looking good?

Changelog Entry :heavy_check_mark:

Package	Changed Files

Changes to files need to be accounted for in their respective changelogs.

Coverage :heavy_check_mark:

File	Coverage

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API leaks :heavy_check_mark:

The following packages contain symbols visible in the public API, but not exported by the library. Export these symbols or remove them from your publicly visible API.

Package	Leaked API symbols

License Headers :heavy_check_mark:

// Copyright (c) 2025, the Dart project authors. Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.

Files
no missing headers

All source files should start with a license header.

Unrelated files missing license headers

Files
pkgs/http/example/main.dart

[brianquinlan]

@natebosch Is this something that you intend to land?