fix(web-runtime): focus follows the caret to the field it types into

Mirrors the driver, so the two hosts agree about focus on a Compose page.
The harness inherits custom properties down the parent chain the way CSS
does, so an implementation matching the inline style attribute fails.

pkg/spec/test/web-dom-harness.ts

@@ -54,6 +54,12 @@ export interface FakeElementSpec {
   // host decides an element is scrollable.
   overflows?: boolean;
   focused?: boolean;
+  // customProperties are DECLARED on this element and INHERITED by everything
+  // under it, which is the whole reason the runtime reads a computed style and
+  // not the style attribute: Compose declares the caret's box on the container
+  // that positions its backing input, and only the input's COMPUTED style
+  // carries it.
+  customProperties?: Record<string, string>;
   children?: FakeElementSpec[];
   shadow?: FakeElementSpec[];
 }
@@ -163,6 +169,14 @@ function activeElementIn(nodes: FakeElement[]): FakeElement | null {
   return null;
 }
 
+function inheritedProperty(element: FakeElement, name: string): string {
+  for (let node: FakeElement | null = element; node; node = node.parentElement) {
+    const declared = node.customProperties?.[name];
+    if (declared !== undefined) return declared;
+  }
+  return "";
+}
+
 function queryScope(scope: { children: FakeElement[] }, selector: string): FakeElement[] {
   const found: FakeElement[] = [];
   const walk = (nodes: FakeElement[]): void => {
@@ -303,9 +317,13 @@ export function withFakeDocument(elements: FakeElement[], run: () => void): void
   const global = globalThis as Record<string, unknown>;
   const originalDocument = global.document;
   const originalWindow = global.window;
+  const originalComputedStyle = global.getComputedStyle;
   const document: FakeRoot = fakeRoot(elements);
   global.document = document;
   global.window = {};
+  global.getComputedStyle = (element: FakeElement) => ({
+    getPropertyValue: (name: string) => inheritedProperty(element, name),
+  });
   __testing__.resetTargetCache();
   try {
     run();
@@ -313,5 +331,6 @@ export function withFakeDocument(elements: FakeElement[], run: () => void): void
     __testing__.resetTargetCache();
     global.document = originalDocument;
     global.window = originalWindow;
+    global.getComputedStyle = originalComputedStyle;
   }
 }

pkg/spec/test/web-runtime.test.ts

@@ -1023,6 +1023,73 @@ test("ax.find reports focus on the field inside the shadow root, not on its host
   });
 });
 
+// Descending the shadow roots is still not enough on Compose for Web: it takes
+// keystrokes on a 1px input pinned to the caret, a SIBLING of the accessibility
+// tree, so DOM focus never reaches the semantics element carrying the test tag
+// and every field read unfocused. internal/driver/chrome/driver.go re-attributes
+// focus to the field the caret sits in, and TestElementState_FocusFollowsTheCaretToItsField
+// pins it there over a real Compose-shaped page.
+//
+// Both fields are focused in turn, because answering with the first editable in
+// the tree would satisfy the email half and still name the wrong field. The
+// password caret overhangs its box, as it does whenever the text style is taller
+// than the field's layout box, so requiring the caret to be CONTAINED rather
+// than to have its centre inside would drop that field back to unfocused.
+test("focus follows the caret to the field it types into, not the input it is", () => {
+  const carets = [
+    { field: "EmailField", y: 78, height: 17.578125 },
+    { field: "PasswordField", y: 157, height: 20 },
+  ];
+  for (const caret of carets) {
+    const app = fakeElement({
+      tag: "div", x: 0, y: 0, width: 760, height: 800, id: "app",
+      shadow: [
+        {
+          tag: "div", x: 0, y: 0, width: 0, height: 0, id: "caret-holder",
+          customProperties: {
+            "--compose-internal-web-backing-input-left": "34",
+            "--compose-internal-web-backing-input-top": String(caret.y),
+            "--compose-internal-web-backing-input-width": "1",
+            "--compose-internal-web-backing-input-height": String(caret.height),
+          },
+          children: [
+            {
+              tag: "input", x: 34, y: caret.y, width: 1, height: caret.height,
+              id: "caret-input", editable: true, focused: true,
+            },
+          ],
+        },
+        {
+          tag: "div", x: 0, y: 0, width: 760, height: 800, id: "a11y-root",
+          children: [
+            {
+              tag: "div", x: 34, y: 78, width: 688, height: 18, id: "EmailField",
+              attrs: { role: "textbox", contenteditable: "true" }, editable: true,
+            },
+            {
+              tag: "div", x: 34, y: 158, width: 688, height: 18, id: "PasswordField",
+              attrs: { role: "textbox", contenteditable: "true" }, editable: true,
+            },
+          ],
+        },
+      ],
+    });
+    withFakeDocument([app], () => {
+      __testing__.extractors.length = 0;
+      const ids = ["EmailField", "PasswordField", "caret-input", "caret-holder", "a11y-root", "app"];
+      for (const id of ids) {
+        __testing__.runtime.extract((state) => {
+          const ax = (state as { ax: { find(s: unknown): Record<string, unknown> | undefined } }).ax;
+          return ax.find(`id:${id}`)?.focused;
+        });
+      }
+      const values = __testing__.evaluateExtractors();
+      const focused = ids.filter((_, index) => readingOf(values, index) === true);
+      assert.deepEqual(focused, [caret.field]);
+    });
+  }
+});
+
 // A nested undefined is the one reading shape the two hosts do NOT encode
 // alike, and this pins the split instead of hiding it. JSON has no undefined,
 // so the key goes with the value here; goja marshals the same member as null,