feat(analytics): build-time bake + telemetry depth (#336)

Bake PostHog + Sentry into the published Docker image (SNAPOTTER_ANALYTICS
build arg, codegen script). Delete entire consent system. Move event emission
to BullMQ worker. Add cross-tier identity stitching, Sentry performance
tracing on both tiers, frontend funnel events. Fix stateful regex bug.

86 files changed, 1593 insertions(+), 3747 deletions(-)

apps/web/src/pages/home-page.tsx

@@ -1,5 +1,5 @@
 import type { Tool } from "@snapotter/shared";
-import { CATEGORIES, SECTIONS, TOOLS, toolSection } from "@snapotter/shared";
+import { ANALYTICS_EVENTS, CATEGORIES, SECTIONS, TOOLS, toolSection } from "@snapotter/shared";
 import { ChevronDown, Search, X } from "lucide-react";
 import { useCallback, useEffect, useMemo, useRef, useState } from "react";
 import { Link, useLocation, useNavigate } from "react-router-dom";
@@ -85,6 +85,16 @@ export function HomePage() {
 
   const searchResults = useFuseSearch(visibleTools, search);
 
+  useEffect(() => {
+    if (!search || search.length < 2) return;
+    const timer = setTimeout(() => {
+      import("@/lib/analytics").then(({ track }) => {
+        track(ANALYTICS_EVENTS.SEARCH, { query: search, results_count: searchResults.length });
+      });
+    }, 1000);
+    return () => clearTimeout(timer);
+  }, [search, searchResults.length]);
+
   const tabTools = useMemo(() => {
     if (activeTab === "all") return visibleTools;
     return visibleTools.filter((tool) => toolSection(tool) === activeTab);