fix(sse): keep Responses continuity when input would ship empty

[Laksopan23]

Summary

• Inject a placeholder user item into Responses input when chat→Responses translation would otherwise ship input: [] with no conversation/continuity field (GitHub Copilot default chat 400: One of input or previous_response_id or '''prompt''' or '''conversation''' must be provided.).
• Under auto Responses state policy, keep previous_response_id when input is empty (explicit strip mode still strips).

Root cause: chat→Responses translation can emit input: [] while responsesStatePolicy (mode auto + store-off) strips previous_response_id, leaving a body with neither field. Reverse direction already had a placeholder guard.

Test plan

• TDD: failing tests first (responses-state-policy.test.ts keep-on-empty, new translator-openai-responses-empty-input-github-400.test.ts)
• npm run test:vitest — 482/482 PASS
• chat-pipeline.test.ts — 29/29 PASS
• Focused suites: responses-handler, responses-state-policy, empty-input-github-400, empty-input-419, strip-store-responses, orphaned-tool-filter, chat-previous-response-id-preserve-mode
• Focused eslint on changed files — 0 errors

⚠️ base-red inherited: #14547

Files

• open-sse/translator/request/openai-responses/toResponses.ts — placeholder inject
• open-sse/utils/responsesStatePolicy.ts — keep previous_response_id when input empty under auto
• tests updated/added

[diegosouzapw]

Clean fix for both sides of the empty-input GitHub Copilot 400 — nice touch mirroring the
already-existing reverse-direction placeholder guard (9router#419) instead of inventing a new
pattern. Traced the call order between the translator and responsesStatePolicy and the two
guards don't conflict. Wasn't able to run the suite this round due to devbox contention.
Only pre-merge item: please add a changelog.d fragment.

[Laksopan23]

Rebased onto 7d23bcf8ec and force-pushed to re-trigger CI (old runs were stuck at action_required).

Local verification (green)

• translator-openai-responses-empty-input-github-400.test.ts + responses-state-policy.test.ts: 12/12 pass
• responses-handler.test.ts filtered to our change: pass
• Diff vs base is only the 5 intended files (toResponses.ts, responsesStatePolicy.ts, + 3 tests)

CI failures — all base-red inherited (⚠️ base-red inherited: #14547)

None of these touch files in this PR:

Job	Failure	Why not ours
API Route Typecheck	auggie.ts TS2769/TS18047, projectCombo.ts TS2459/TS2724	Not in this diff
Docs Gates	check:env-doc-sync: DEEP_HEALTH_CHECK_ENABLED missing from .env.example	Not in this diff
Unit Tests 1–4	e.g. qwen38-max-bare-id-alias.test.ts, credential-path map deepEqual	Not in this diff
Fast Quality Gates	gates deps file-size mutation-test-coverage open-sse-typecheck typecheck:core	Base tip red (see #14547)
responses-handler.test.ts keepalive assertion	expects bare {"type":"response.in_progress"}; base emits #14330 frame with sequence_number+response	Reproduced on pure base checkout @ 7d23bcf8ec

Green here: Vitest, No new ESLint warnings, Merge integrity, Change Classification, semgrep, semgrep-cloud.

Please merge only after base-red clears (#14547) or with explicit operator override — do not chase these failures in this PR.