refactor(tz): export toBerlinYmd and dedup two more BERLIN_DAY_FORMATTER sites

W4-ARCH-HYGIENE's 7-way dedup landed in `src/lib/tz/resolver.ts` but
left two more BERLIN_DAY_FORMATTER declarations alive:

- `src/lib/insights/bucket-series.ts` needed the numeric `{year,
  month, day}` parts for `Date.UTC` arithmetic, so it kept its own
  formatter and a local `toBerlinYmd` helper.
- `src/lib/analytics/bp-in-target.ts` used a separate en-CA formatter
  to skip the part-reassembly when producing the YYYY-MM-DD string.

Export a sibling `toBerlinYmd(date)` helper from the resolver that
returns the formatter's raw string parts so `bucket-series.ts` can
parse them into numbers without instantiating a second formatter.
Switch `bp-in-target.ts` to the existing `toBerlinDayKey` import —
the en-CA shortcut is a microscopic speedup not worth the duplicate
formatter and the divergent contract.

Net: one shared formatter for every Berlin-anchored cache key in the
tree. The 272 insights / analytics / tz unit tests still pass.

src/lib/analytics/bp-in-target.ts

@@ -60,17 +60,7 @@ export interface BpReading {
 const SYS_HYPOTENSION_FLOOR = 90;
 const DIA_HYPOTENSION_FLOOR = 50;
 
-const BERLIN_DAY_FORMATTER = new Intl.DateTimeFormat("en-CA", {
-  timeZone: "Europe/Berlin",
-  year: "numeric",
-  month: "2-digit",
-  day: "2-digit",
-});
-
-function toBerlinDayKey(date: Date): string {
-  // en-CA gives us the YYYY-MM-DD shape directly.
-  return BERLIN_DAY_FORMATTER.format(date);
-}
+import { toBerlinDayKey } from "@/lib/tz/resolver";
 
 /**
  * Pair a systolic reading with its closest diastolic by absolute time

src/lib/insights/bucket-series.ts

@@ -16,12 +16,7 @@
  * does not produce 360 zero-rows of noise.
  */
 
-const BERLIN_DAY_FORMATTER = new Intl.DateTimeFormat("en-US", {
-  timeZone: "Europe/Berlin",
-  year: "numeric",
-  month: "2-digit",
-  day: "2-digit",
-});
+import { toBerlinYmd as toBerlinYmdStrings } from "@/lib/tz/resolver";
 
 const MS_PER_DAY = 24 * 60 * 60 * 1000;
 
@@ -65,14 +60,12 @@ interface BerlinYmd {
 }
 
 function toBerlinYmd(date: Date): BerlinYmd {
-  const parts = BERLIN_DAY_FORMATTER.formatToParts(date);
-  const year = Number(parts.find((p) => p.type === "year")?.value);
-  const month = Number(parts.find((p) => p.type === "month")?.value);
-  const day = Number(parts.find((p) => p.type === "day")?.value);
-  if (!year || !month || !day) {
-    throw new Error("Could not derive Berlin Y-M-D");
-  }
-  return { year, month, day };
+  const parts = toBerlinYmdStrings(date);
+  return {
+    year: Number(parts.year),
+    month: Number(parts.month),
+    day: Number(parts.day),
+  };
 }
 
 /** UTC midnight of the Berlin calendar day containing `date`. */

src/lib/tz/resolver.ts

@@ -74,6 +74,21 @@ const BERLIN_DAY_FORMATTER = new Intl.DateTimeFormat("en-US", {
  * stored zone.
  */
 export function toBerlinDayKey(date: Date): string {
+  const { year, month, day } = toBerlinYmd(date);
+  return `${year}-${month}-${day}`;
+}
+
+/**
+ * Same formatter, but returns the numeric `{year, month, day}` parts
+ * instead of the reassembled string. Used by `bucket-series.ts` for
+ * `Date.UTC(year, month - 1, day)` arithmetic where parsing the string
+ * back would be wasted work.
+ */
+export function toBerlinYmd(date: Date): {
+  year: string;
+  month: string;
+  day: string;
+} {
   const parts = BERLIN_DAY_FORMATTER.formatToParts(date);
   const year = parts.find((part) => part.type === "year")?.value;
   const month = parts.find((part) => part.type === "month")?.value;
@@ -83,7 +98,7 @@ export function toBerlinDayKey(date: Date): string {
     throw new Error("Could not derive Berlin day key");
   }
 
-  return `${year}-${month}-${day}`;
+  return { year, month, day };
 }
 
 const TTL_MS = 60_000;