fix(segment-button): update checked state on render (#26970)

<!-- Please refer to our contributing documentation for any questions on
submitting a pull request, or let us know here if you need any help:
https://ionicframework.com/docs/building/contributing -->

## Pull request checklist

Please check if your PR fulfills the following requirements:
- [ ] Tests for the changes have been added (for bug fixes / features)
- [ ] Docs have been reviewed and added / updated if needed (for bug
fixes / features)
- Some docs updates need to be made in the `ionic-docs` repo, in a
separate PR. See the [contributing
guide](https://github.com/ionic-team/ionic-framework/blob/main/.github/CONTRIBUTING.md#modifying-documentation)
for details.
- [x] Build (`npm run build`) was run locally and any changes were
pushed
- [x] Lint (`npm run lint`) has passed locally and any fixes were made
for failures


## Pull request type

<!-- Please do not submit updates to dependencies unless it fixes an
issue. -->

<!-- Please try to limit your pull request to one type, submit multiple
pull requests if needed. -->

Please check the type of change your PR introduces:
- [x] Bugfix
- [ ] Feature
- [ ] Code style update (formatting, renaming)
- [ ] Refactoring (no functional changes, no api changes)
- [ ] Build related changes
- [ ] Documentation content changes
- [ ] Other (please describe): 


## What is the current behavior?
<!-- Please describe the current behavior that you are modifying. -->

In v7, asynchronously assigning a value to `ion-segment` and
`ion-segment-button` can cause the `ion-segment` to render without an
active value (segment button does not show as checked).

<!-- Issues are required for both bug fixes and features. -->
Issue URL: resolves #26830


## What is the new behavior?
<!-- Please describe the behavior or changes that are being added by
this PR. -->

- The `ion-segment-button` checked state is synced with the parent
`ion-segment`, when the component finishes the initial render.

## Does this introduce a breaking change?

- [ ] Yes
- [x] No

<!-- If this introduces a breaking change, please describe the impact
and migration path for existing applications below. -->


## Other information

<!-- Any other information that is important to this PR such as
screenshots of how the component looks before and after the change. -->

Dev-build: `7.0.0-dev.11678736268.18a0beb1` ✅

---------

Co-authored-by: Liam DeBeasi <liamdebeasi@users.noreply.github.com>

core/src/components/segment/test/segment.spec.ts

@@ -16,3 +16,23 @@ it('should disable segment buttons added to disabled segment async', async () =>
   const segmentButton = page.body.querySelector('ion-segment-button');
   expect(segmentButton.disabled).toBe(true);
 });
+
+it('should set checked state when value is set asynchronously', async () => {
+  const page = await newSpecPage({
+    components: [Segment, SegmentButton],
+    html: `
+      <ion-segment value="first">
+        <ion-segment-button>First</ion-segment-button>
+      </ion-segment>
+    `,
+  });
+
+  const segmentButton = page.root.querySelector('ion-segment-button');
+
+  expect(segmentButton.classList.contains('segment-button-checked')).toBe(false);
+
+  segmentButton.value = 'first';
+  await page.waitForChanges();
+
+  expect(segmentButton.classList.contains('segment-button-checked')).toBe(true);
+});