MVP M6: live Socrates dock — LLM gateway + persisted thread + reply loop

The dock now talks to a real LLM. On first load it asks Socrates for an
opening turn that's grounded in the project's actual SysML model + active
validation issues. User replies and option-picks send turns through the
same channel. Thread + every message persist in SQLite so refresh keeps
the conversation.

apps/web/lib/llm
- gateway.ts: LLMGateway interface (chat + ChatOptions). Two adapters:
    - lmstudio: OpenAI SDK against LMSTUDIO_BASE_URL (default
      http://localhost:1234/v1)
    - anthropic: @anthropic-ai/sdk against claude-sonnet-4-6 (set
      ANTHROPIC_API_KEY when LLM_PROVIDER=anthropic)
  Provider chosen via LLM_PROVIDER env (default: lmstudio).
- chatJSON(): JSON-mode helper with parse-error repair-retry — the same
  defensive pattern proven against gemma-4-e4b in Phase 0.
- prompts.ts: server-only loader that caches .md prompts.
- prompts/socrates/character.md + review.md: ported verbatim from
  phase-0/src/prompts/ (Phase 0 corpus validated these 10/10).
- socrates.ts: sendUserTurn() — builds the system prompt (character +
  review + project context with trimmed model + active issues), runs
  chatJSON against the gateway, persists user + assistant turns,
  returns the structured turn. SocratesTurn schema is { text, options? }
  with up to 3 numbered options matching the prototype.

apps/web/prisma
- SocratesThread + SocratesMessage tables. Auto-create one open thread
  per project on first load.

apps/web/app/api/projects/[projectId]/socrates
- GET: returns active thread + parsed messages.
- POST: body { text }. Empty text triggers an opening turn. Persists user
  + assistant turns, returns assistant turn + provider metadata.

apps/web/components/socrates/SocratesDock.tsx
- Replaces the static thread prop with a projectId. Loads from API on
  mount, auto-triggers an opening turn if the thread is empty, sends
  user replies via POST. Numbered options click-to-pick or 1–3 keyboard
  shortcut (skipped when focus is in an input). Status line shows the
  active provider + model. Optimistic-local: user message appears
  instantly, "thinking…" placeholder shows while the LLM works, errors
  surface inline.

apps/web/.env.example + .env.local
- LLM_PROVIDER, LMSTUDIO_BASE_URL/MODEL/API_KEY, ANTHROPIC_API_KEY/MODEL.
- .env.local committed only with the local default (no real secrets);
  user supplies their own per-machine.

What's not yet here (next iterations):
- Streaming responses (currently waits for full response, ~5-15s)
- Multi-thread switcher (one auto-thread per project)
- Socrates-proposes-ops flow (M7)

apps/web/styles/base.css

@@ -1059,3 +1059,38 @@ button { font-family: inherit; }
 }
 .chip-rename:focus { background: var(--surface-2); }
 .chip.chip-editing { box-shadow: 0 0 0 1.5px var(--accent); }
+
+/* ─── Dock input (M6) ─── */
+.dock-input { display: flex; align-items: center; gap: 6px; }
+.dock-input-field {
+  flex: 1;
+  border: none;
+  background: transparent;
+  outline: none;
+  font: inherit;
+  font-family: var(--font-prose);
+  font-size: 12.5px;
+  color: var(--fg);
+  min-width: 0;
+}
+.dock-input-field::placeholder { color: var(--muted); }
+.dock-input-field:disabled { color: var(--muted); cursor: not-allowed; }
+.dock-input-send {
+  background: transparent;
+  border: 1px solid var(--border-strong);
+  border-radius: 4px;
+  padding: 2px 6px;
+  font-family: var(--font-mono);
+  font-size: 10px;
+  color: var(--muted);
+  cursor: pointer;
+}
+.dock-input-send:hover:not(:disabled) {
+  background: var(--accent);
+  color: var(--accent-on);
+  border-color: var(--accent);
+}
+.dock-input-send:disabled {
+  opacity: 0.4;
+  cursor: not-allowed;
+}