Add codex2api as a protocol-first OAuth source

This keeps the existing CPA, SUB2API, and contribution flows intact
while introducing codex2api as a separate source that plugs into
Step 7 and Step 10 through backend APIs instead of page DOM.

The sidepanel now exposes codex2api settings, preserves the built-in
local default through placeholder-only UI, and accepts user-provided
public admin URLs. Step 7 now treats missing or invalid management
secrets as terminal config errors so the flow stops instead of retrying
needlessly.

Constraint: New source must be additive and must not break existing CPA/SUB2API/contribution paths
Rejected: Drive codex2api through admin page button clicks | too brittle against frontend DOM changes
Rejected: Reuse contribution mode as a source surface | violates existing panelMode/runtime-mode boundary
Confidence: high
Scope-risk: moderate
Reversibility: clean
Directive: Keep codex2api on the protocol path unless its API becomes insufficient; do not add a panel content script without proving the protocol path cannot work
Tested: npm test; targeted codex2api/auth retry loops repeated 40 times; full suite repeated 5 times
Not-tested: Real browser run against a live codex2api instance with a real Admin Secret and OpenAI authorization

background/message-router.js

@@ -121,6 +121,8 @@
           if (payload.sub2apiGroupId !== undefined) updates.sub2apiGroupId = payload.sub2apiGroupId || null;
           if (payload.sub2apiDraftName !== undefined) updates.sub2apiDraftName = payload.sub2apiDraftName || null;
           if (payload.sub2apiProxyId !== undefined) updates.sub2apiProxyId = payload.sub2apiProxyId || null;
+          if (payload.codex2apiSessionId !== undefined) updates.codex2apiSessionId = payload.codex2apiSessionId || null;
+          if (payload.codex2apiOAuthState !== undefined) updates.codex2apiOAuthState = payload.codex2apiOAuthState || null;
           if (Object.keys(updates).length) {
             await setState(updates);
           }