Explicitly declare supported public APIs with '__all__'

### Feature Request / Improvement

Currently, we rely on the informal naming conventions (with or without underscore) to distinguish between a public or private API.

It will be helpful to declare the names of public APIs in the `__all__` attribute on all our public API supporting modules as it will:
- control what APIs we expose to wildcard imports
- enhance discoverability of public APIs (when reading the source code as users or developers)
- and allow tools like [Griffe](https://mkdocstrings.github.io/griffe/guide/users/navigating/#object-visibility) to detect the correct public APIs for backwards compatibility analysis in our CI

Start by identifying the modules that support the public API and reviewing their current naming conventions. Add __all__ declarations for the intended public names, then verify wildcard imports and confirm that Griffe detects the same API surface for compatibility analysis.

Written by the indexing model from the issue text.