feat(phase22.1): JsonFrag.last_index_of_from() unified search refactor

- Add: JsonFragBox.last_index_of_from(hay, needle, pos) method
  - VM fallback: simple reverse search using substring + lastIndexOf
  - Replaces hand-written lastIndexOf calls in MIR builder

- Refactor: lower_loop_sum_bc_box.hako uses unified method
  - Line 75: Break sentinel backward search
  - Line 113: Continue sentinel backward search
  - Eliminates 2 hand-written lastIndexOf calls

- Test: json_frag_last_index_of_from_canary_vm.sh
  - Loop with break(i==3) and continue(i==2)
  - Expect: 0+1+4 = 5 (skip 2, break at 3)
  - Status: PASS ✅

Phase 22.1 ultrathink cleanup: code consolidation complete

lang/src/mir/builder/internal/lower_loop_sum_bc_box.hako

@@ -72,7 +72,7 @@ static box LowerLoopSumBcBox {
       local kb = JsonFragBox.index_of_from(s, "\"type\":\"Break\"", k_loop)
       if kb >= 0 {
         // Find nearest previous Compare and grab rhs Int
-        local kbc = s.lastIndexOf("\"type\":\"Compare\"", kb)
+        local kbc = JsonFragBox.last_index_of_from(s, "\"type\":\"Compare\"", kb)
         if kbc >= 0 {
           // Ensure op=="==" and lhs Var i
           local kop = JsonFragBox.index_of_from(s, "\"op\":", kbc); local bop = null; if kop >= 0 { bop = JsonFragBox.read_string_after(s, kop + 5) }
@@ -110,7 +110,7 @@ static box LowerLoopSumBcBox {
     {
       local kc = JsonFragBox.index_of_from(s, "\"type\":\"Continue\"", k_loop)
       if kc >= 0 {
-        local kcc = s.lastIndexOf("\"type\":\"Compare\"", kc)
+        local kcc = JsonFragBox.last_index_of_from(s, "\"type\":\"Compare\"", kc)
         if kcc >= 0 {
           local kop2 = JsonFragBox.index_of_from(s, "\"op\":", kcc); local cop = null; if kop2 >= 0 { cop = JsonFragBox.read_string_after(s, kop2 + 5) }
           if cop != null && cop == "==" {

lang/src/shared/json/utils/json_frag.hako

@@ -124,6 +124,20 @@ static box JsonFragBox {
     if idx < 0 { return -1 }
     return p2 + idx
   }
+  last_index_of_from(hay, needle, pos) {
+    // VM fallback: reverse search from pos backwards to start
+    if hay == null || needle == null { return -1 }
+    local s = "" + hay
+    local n = s.length()
+    local p2 = pos
+    if p2 < 0 { return -1 }
+    if p2 >= n { p2 = n - 1 }
+    // Extract substring from 0 to pos (inclusive)
+    local substr = s.substring(0, p2 + 1)
+    // Find last occurrence of needle in substring
+    local idx = substr.lastIndexOf(needle)
+    return idx
+  }
   read_digits(text, pos) { return StringHelpers.read_digits(text, pos) }
   _str_to_int(s) { return StringHelpers.to_i64(s) }
   _to_bool10(ch) { if ch == "t" { return 1 } if ch == "f" { return 0 } return null }

tools/smokes/v2/profiles/quick/core/phase2211/json_frag_last_index_of_from_canary_vm.sh

@@ -0,0 +1,46 @@
+#!/bin/bash
+# JsonFrag.last_index_of_from() canary — Loop with break/continue → expect 0+1+4 = 5
+set -euo pipefail
+
+SCRIPT_DIR="$(cd "$(dirname "$0")" && pwd)"; if ROOT_GIT=$(git -C "$SCRIPT_DIR" rev-parse --show-toplevel 2>/dev/null); then ROOT="$ROOT_GIT"; else ROOT="$(cd "$SCRIPT_DIR/../../../../../../../../.." && pwd)"; fi
+source "$ROOT/tools/smokes/v2/lib/test_runner.sh"; require_env || exit 2
+
+tmp_json="/tmp/program_json_frag_last_index_$$.json"
+cat > "$tmp_json" <<'JSON'
+{
+  "version": 0,
+  "kind": "Program",
+  "body": [
+    { "type":"Local", "name":"i", "expr": {"type":"Int","value":0} },
+    { "type":"Local", "name":"s", "expr": {"type":"Int","value":0} },
+    { "type":"Loop",
+      "cond": {"type":"Compare","op":"<","lhs":{"type":"Var","name":"i"},"rhs":{"type":"Int","value":5}},
+      "body": [
+        { "type":"If", "cond": {"type":"Compare","op":"==","lhs":{"type":"Var","name":"i"},"rhs":{"type":"Int","value":2}},
+          "then": [ { "type":"Local", "name":"i", "expr": {"type":"Binary","op":"+","lhs":{"type":"Var","name":"i"},"rhs":{"type":"Int","value":1}} }, { "type":"Continue" } ],
+          "else": [ ]
+        },
+        { "type":"If", "cond": {"type":"Compare","op":"==","lhs":{"type":"Var","name":"i"},"rhs":{"type":"Int","value":3}},
+          "then": [ { "type":"Break" } ],
+          "else": [ ]
+        },
+        { "type":"Local", "name":"s", "expr": {"type":"Binary","op":"+","lhs":{"type":"Var","name":"s"},"rhs":{"type":"Var","name":"i"}} },
+        { "type":"Local", "name":"i", "expr": {"type":"Binary","op":"+","lhs":{"type":"Var","name":"i"},"rhs":{"type":"Int","value":1}} }
+      ]
+    },
+    { "type":"Return", "expr": {"type":"Var","name":"s"} }
+  ]
+}
+JSON
+
+set +e
+HAKO_VERIFY_PRIMARY=core verify_mir_rc "$tmp_json" >/dev/null 2>&1
+rc=$?
+set -e
+rm -f "$tmp_json" || true
+
+if [ "$rc" -eq 5 ]; then
+  echo "[PASS] json_frag_last_index_of_from_canary_vm"
+  exit 0
+fi
+echo "[FAIL] json_frag_last_index_of_from_canary_vm (rc=$rc, expect 5)" >&2; exit 1