Epic C: State architecture baseline

[mjkatgithub]

Goal

Introduce focused Pinia stores where local component/composable state is no
longer sufficient for robust startup and runtime behavior.

Scope

• Pinia baseline for auth/session state
• Pinia baseline for chat runtime state

Definition of Done

• All sub-issues are created and linked to this epic
• Each sub-issue has acceptance criteria and test checklist
• Store boundaries and responsibilities are documented