fix(rewrite): auth refresh for rewrite requests

[gabeqt]

Summary

Fixes ChatGPT Subscription chat rewrite requests failing with 401 Unauthorized. The /api/rewrite endpoint now resolves the session’s owner scoped authentication before starting the model stream. Adds a regression test which verifies that the resolved authorization header is used by the rewrite request.

Target branch

• This PR targets dev, not main. All PRs land in dev; main is curated by the maintainer at each release. If your PR is on main by accident, click "Edit" on this PR and change the base.

Linked Issue

Fixes #5738

Type of Change

• Bug fix (non-breaking — fixes a confirmed issue)
• New feature (non-breaking — adds new behaviour)
• Breaking change (changes or removes existing behaviour)
• Refactor / cleanup (behaviour unchanged)
• Documentation only
• CI / tooling / configuration

Checklist

• I searched open issues and open PRs — this is not a duplicate.
• This PR targets dev
• My changes are limited to the scope described above — no unrelated refactors or whitespace changes mixed in.
• I actually ran the app (docker compose up or uvicorn app:app) and verified the change works end-to-end. Type-checks and unit tests are not enough.

How to Test

1. Configure and connect a ChatGPT Subscription provider.
2. Start a chat and receive an assistant response.
3. Use Rewrite shorter or Explain simpler on that response.
4. Confirm the rewritten response streams successfully without errors.

Visual / UI changes — REQUIRED if you touched anything that renders

Anything that changes what the UI looks like — buttons, icons, padding, colors, fonts, spacing, layout, CSS, HTML, SVG, or any static/js/ module that draws to the DOM — needs all of the following. PRs that change rendering without these WILL be closed.

No UI changes

• Screenshot or short clip of the change in the running app, attached below. Mobile screenshot too if the change affects mobile.
• Style match: the change uses Odysseus's existing visual language. Specifically:
  • Reuse existing CSS variables (--red, --fg, --bg, --card, --border, etc.) — do not introduce new color values, font sizes, or spacing units.
  • Reuse existing button/input/card/border classes. Don't invent parallel styling.
  • No Unicode emoji in UI or code. Use inline SVG (matching the monochrome icon style already in static/index.html) or plain text.
  • Monospaced font (Fira Code) for primary UI text. Don't override.
  • Dark theme is the default; any light-mode work must be wired through the existing theme system, not hard-coded.
• No new component patterns. If a similar widget already exists in the app, extend it instead of writing a parallel one.
• I am not an LLM agent submitting a bulk PR. If you are, please open an issue describing the problem first — bulk auto-generated PRs that don't match the project's visual style are closed on sight, even when the underlying fix is correct.

Screenshots / clips