Support OAuth authentication for Anthropic and OpenAI

Self-hosted Inbox Zero currently requires direct API keys for LLM providers. Users with existing subscriptions to Claude Max or ChatGPT Pro already have authenticated access to these models through OAuth, but Inbox Zero can't use those sessions. This forces users to create separate API keys and manage additional billing.

Proposed solution:

Support OAuth-based authentication for Anthropic and OpenAI as an alternative to API keys.

Both providers are moving toward OAuth as a first-class auth method. Claude Code and other tools already use Anthropic OAuth. Supporting this would let self-hosted users point Inbox Zero at their existing subscriptions instead of paying separately for API access.

Alternatives considered:

Running a local proxy that translates OAuth tokens to API-key-style requests. It works but adds latency and maintenance overhead.