[objective_c] Make all API types public

[liamappelbe]

A lot of types that are exposed in the package:objective_c API start with a _. This causes problems for users in some cases, such as making it hard write mocks. This also fix the API leaks health check.

#1864
Fixes #1863
Fixes #1862
Fixes #1861

[github-actions]

PR Health

Breaking changes ✔️

Package	Change	Current Version	New Version	Needed Version	Looking good?
objective_c	Breaking	4.1.0	5.0.0-wip	5.0.0	✔️

Changelog Entry ✔️

Package	Changed Files

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

API leaks ✔️

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 ✔️

// 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/jni/lib/src/third_party/generated_bindings.dart
pkgs/objective_c/lib/src/ns_input_stream.dart

[coveralls]

coverage: 87.49% (+0.06%) from 87.434%
when pulling f0a810a on private_types
into 87ef391 on main.