feat(gui): opt in custom Responses plaintext reasoning replay

[lidge-jun]

Summary

Closes #6675.

• Add a default-off plaintext reasoning replay checkbox to custom Responses provider creation and Settings. Explain that enabling it sends previous reasoning to the endpoint and can increase token use; local/key custom destinations are eligible, and curated/OpenAI/Azure/OAuth/forward surfaces keep their current behavior.
• Persist explicit true/false choices through the existing capability, validate boolean/null PATCH values, and retain omitted configuration only when an overwrite keeps the same destination. Hidden stale form values do not enter create or update payloads.
• Update all eleven GUI locales and the provider/management documentation.

Verification

• Red baseline: new server regression 3 pass / 4 fail; new UI regression 5 pass / 3 fail. Green: server replay/persistence 30 pass; GUI replay plus live-model provenance 16 pass; carry/layout/ratchet/Lab guards 74 pass.
• OCX_TEST_NO_QUEUE=1 bun run test:changed --parallel=1 tests/server/management-provider-responses-reasoning.test.ts tests/server/management-provider-compat-carry.test.ts tests/providers/deepseek-reasoning-replay.test.ts tests/gui/provider-payload.test.ts: 45 pass / 0 fail across 3 selected files. The new management file is also exercised explicitly in the 30-test focused run. The initial queued attempt was stopped before execution while another lane held the user lock; only this bounded single-worker run intentionally overlapped.
• bun run typecheck, GUI i18n/lint/build, bun run structure:check, bun run privacy:scan, and docs build passed (569 pages; 79,332 links).
• Real ProviderSettings component browser smoke: checkbox defaults off, explicit enable/save callback produced preserveResponsesReasoningContent:true and retained checked state. Screenshot uses a scratch harness with a parent Save action; no credentials or screenshot files are committed to this branch.
• Full local suite omitted under the repository resource exception due to concurrent worktree test load. Hosted and cross-platform CI are deferred to the coordinator's final integrated run. This draft does not claim those checks pass. Independent gpt-6.1-sol full-diff and security review PASS, no concrete P0-P2 findings, on exact pushed head 2968740475e078b34ba15d1bb3a2bd2648c0fca8 against dev 7af092ca4f78828238b425bf351d5989e237f89f. Independent in-memory adapter/forward/Azure hidden-draft probes also passed.

Checklist

• Scope stays focused and avoids unrelated cleanup.
• Docs or release notes were updated when needed.
• Security-sensitive changes were reviewed for secrets, auth, and unsafe defaults.

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[github-actions]

✅ Deterministic PR hygiene checks passed.

[lidge-jun]

Landed on dev as squashed commit 6c27087518 through the 2.84.0 owner bundle #7009 (merge 8f10f238e3). Ships in 2.84.0.