API route
POST /api/suggest
Ask one Provider for Suggestions, drop invalid ones and Re-check the rest on every Registry.
Send the Name, the Provider id and the Name context (takenOn: the Registries on which the Name is Taken).
The Provider’s Suggestions are filtered by the Name validation rules, then re-checked together: npm, Homebrew and PyPI per Suggestion, GitHub once for all of them. Each Suggestion comes back with its own Registry result per Registry.
An invalid Name gets 400. A Provider that fails gets 503 with its error, so the page can say which Provider failed.