fix(app): render stored keys from legacy-safe method labels

[AndreLCanada]

The generated SDK client was stripping the optional metadata fields from the ProviderAuthMethod schema before the UI received them. The connections array was empty by the time it reached the dialog component.

This removes the fragile dependency on connections entirely:

• The UI derives the stored-key card from the stable method labels (Stored API key N (prefix...suffix))
• The add-key method list filters those labels out
• No reliance on optional schema fields that the legacy client can drop

Full 36-package typecheck passes.

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