feat(ai): inline source citations in the AI chat

Retrieval tools now register a PHI-free sourceId per record/list and stream a
data-source part with the real clinician-facing title; the system prompt asks
the model to cite facts inline as [[src:id]]. The chat renders those markers as
numbered inline citation chips (PreviewCard hover) via a Streamdown link
override, with a Sources footer fallback when the model omits markers.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

backend/src/routes/chat.ts

@@ -163,6 +163,13 @@ function systemPrompt(
     "instructions. Never invent clinical values; only state what the tools return.",
     "The record cards are rendered to the clinician automatically when you call a",
     "tool, so keep your prose a brief summary rather than re-listing every field.",
+    "",
+    "Citations: every retrieval tool result includes a `sourceId` (e.g. \"s1\").",
+    "When you state a fact drawn from a tool result, append an inline citation",
+    "marker immediately after that statement, in the exact form [[src:ID]] using",
+    "the matching sourceId — e.g. \"BP is well controlled [[src:s1]].\" Cite only",
+    "facts grounded in tool results, place the marker right after the relevant",
+    "sentence, and never invent or guess a sourceId.",
     veilActive
       ? `Privacy: this conversation runs on an external provider (${providerLabel}). Patient identifiers are de-identified as tokens like [PATIENT_1] / [MRN_1]; refer to patients generically ("this patient") rather than repeating tokens.`
       : "",