Add isNotLoggedIn() utility to detect unauthenticated state and display
"Not logged in" message in both LogoV2 and CondensedLogo components.
Replace billing type with provider display name (e.g. "OpenAI", "AWS
Bedrock") when logged in. Subscribe to authVersion to re-render on
login/logout. Add third-party provider model options for OpenAI, Gemini,
Grok, Bedrock, Vertex, and Foundry. Disable biome formatter.
