refactor(app): unify provider connect dialog

[Brendonovich]

Summary

• unify provider selection, custom-provider setup, and authentication under one dialog shell
• add a provider connection controller so callers can initialize and own selected-provider state
• let settings-originated flows override Back to return to the Providers settings tab
• migrate existing provider connection entry points to the unified dialog

Validation

• bun typecheck from packages/app
• repository-wide pre-push typecheck
• manually verified Providers settings -> provider picker -> custom provider -> Back returns to Providers settings