disambiguate session provider

[heskew]

resolves #26

[Copilot]

Pull request overview

This PR resolves #26 by disambiguating the OAuth provider stored on the session when using named provider configurations, separating “provider config key” from “provider type” while preserving backwards compatibility.

Changes:

• Extend session OAuth metadata to include providerConfigId (config key) and providerType (provider type), while deprecating provider for the config-key meaning.
• Populate the new session fields during OAuth callback handling and return them from the user-info endpoint.
• Update middleware to resolve providers by providerConfigId (with fallback to provider) and adjust multi-tenant SSO docs example.

Reviewed changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 5 comments.

File	Description
src/types.ts	Adds providerConfigId and providerType to OAuthSessionMetadata and deprecates provider for the config-key meaning.
src/lib/handlers.ts	Writes the new fields into the session during callback; surfaces them in handleUserInfo.
src/index.ts	Uses providerConfigId (fallback to provider) for provider registry lookup and dynamic resolution logging.
docs/multi-tenant-sso.md	Updates example to use providerConfigId as the tenant identifier.

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