fix(verifier): name a web handle by the same ladder as a tree element

The handle fallback read only text, which is textContent and therefore always
empty for an input, so the model could not tell the amount field from the note
field. It now mirrors visibleLabel's ladder rather than introducing a second
naming scheme.

Claude-Session: https://claude.ai/code/session_01A5KmftdEJ49A9z5mF5ESrX

internal/verifier/llm_test.go

@@ -1,6 +1,7 @@
 package verifier
 
 import (
+	"encoding/json"
 	"strings"
 	"testing"
 
@@ -739,3 +740,96 @@ func TestCandidatesAcceptASingleItemAuthoredSampler(t *testing.T) {
 		t.Errorf("sampled tap missing: %v", descriptions(candidates))
 	}
 }
+
+// webFieldTreeJSON is the add-transaction screen as the chrome driver dumps it:
+// two inputs a user tells apart by the <label> bound to each, which the dump
+// does not carry. Named from the tree alone they collapse onto their CSS class.
+const webFieldTreeJSON = `{
+  "attributes": {"tag": "html", "bounds": "[0,0,400,800]"},
+  "children": [
+    {"attributes": {"resource-id": "txn-amount", "tag": "input", "class": "input amount-input", "bounds": "[0,100,400,160]"}, "editable": true, "enabled": true, "children": []},
+    {"attributes": {"resource-id": "txn-note", "tag": "input", "class": "input", "bounds": "[0,200,400,260]"}, "editable": true, "enabled": true, "children": []}
+  ]
+}`
+
+// The web tick evaluates extractors in V8 and injects the handles here, so an
+// authored action's target is a plain object with no selector to resolve
+// against the tree. Naming it by the handle's own text names every input "",
+// and the model then cannot tell the amount field from the note field.
+// pkg/spec/test/web-runtime.test.ts asserts the producing side builds these
+// handles with the hint each assertion here reads.
+func TestCandidatesNameWebAuthoredFieldsByTheirHint(t *testing.T) {
+	const amountHandle = `{
+      "id": "txn-amount", "text": "", "desc": "", "class": "input amount-input",
+      "clickable": true, "enabled": true, "editable": true, "focused": false,
+      "x": 200, "y": 130, "bounds": {"left": 0, "top": 100, "right": 400, "bottom": 160},
+      "attrs": {"tag": "input", "aria-label": "", "id": "txn-amount",
+                "class": "input amount-input", "placeholder": "0.00", "hintText": "Amount"}
+    }`
+	const noteHandle = `{
+      "id": "txn-note", "text": "", "desc": "", "class": "input",
+      "clickable": true, "enabled": true, "editable": true, "focused": false,
+      "x": 200, "y": 230, "bounds": {"left": 0, "top": 200, "right": 400, "bottom": 260},
+      "attrs": {"tag": "input", "aria-label": "", "id": "txn-note", "class": "input",
+                "placeholder": "What's this for?", "hintText": "Note (optional)"}
+    }`
+
+	v := newVerifier(t)
+	loadActionSpec(t, v, `
+		import { InputText, actions, extract } from "@sanderling/spec";
+		const amount = extract((s) => s.ax.find({ id: "txn-amount" })).named("amount");
+		const note = extract((s) => s.ax.find({ id: "txn-note" })).named("note");
+		globalThis.actions = actions(() => {
+			if (!amount.current || !note.current) return [];
+			return [
+				InputText({ into: amount.current, text: "12.34" }),
+				InputText({ into: note.current, text: "Coffee" }),
+			];
+		});
+	`)
+	pushTree(t, v, webFieldTreeJSON)
+	if _, err := v.OverrideExtractorValues(map[int]json.RawMessage{
+		0: json.RawMessage(amountHandle),
+		1: json.RawMessage(noteHandle),
+	}); err != nil {
+		t.Fatal(err)
+	}
+
+	candidates := mustCandidates(t, v, LabelSourceVisibleText)
+	if !hasCandidate(candidates, `Type "12.34" into "Amount"`) {
+		t.Errorf("amount field unnamed: %v", descriptions(candidates))
+	}
+	if !hasCandidate(candidates, `Type "Coffee" into "Note (optional)"`) {
+		t.Errorf("note field unnamed: %v", descriptions(candidates))
+	}
+}
+
+// The identifier arm must stay blind to anything a user reads, hint included.
+func TestCandidatesNameWebAuthoredFieldsByIdentifierOnThatArm(t *testing.T) {
+	const amountHandle = `{
+      "id": "txn-amount", "text": "", "editable": true, "enabled": true,
+      "x": 200, "y": 130,
+      "attrs": {"tag": "input", "hintText": "Amount"}
+    }`
+	v := newVerifier(t)
+	loadActionSpec(t, v, `
+		import { InputText, actions, extract } from "@sanderling/spec";
+		const amount = extract((s) => s.ax.find({ id: "txn-amount" })).named("amount");
+		globalThis.actions = actions(() =>
+			amount.current ? [InputText({ into: amount.current, text: "12.34" })] : []);
+	`)
+	pushTree(t, v, webFieldTreeJSON)
+	if _, err := v.OverrideExtractorValues(map[int]json.RawMessage{
+		0: json.RawMessage(amountHandle),
+	}); err != nil {
+		t.Fatal(err)
+	}
+
+	candidates := mustCandidates(t, v, LabelSourceResourceID)
+	if !hasCandidate(candidates, `Type "12.34" into "txn-amount"`) {
+		t.Errorf("identifier arm lost the field name: %v", descriptions(candidates))
+	}
+	if hasCandidate(candidates, `Type "12.34" into "Amount"`) {
+		t.Error("identifier arm leaked the hint a user reads")
+	}
+}