chore(deps): add playwright-core as a dev dependency (#30827)

This updates the `package-lock` file to match the structure `next` uses
so we won't have a mismatch with errors on each branch. It installs
`playwright-core` as a dev dependency to align with `next`.

How to test this:

1. Switch to this branch `chore/deps-playwright`
1. Remove `node_modules`: `rm -rf node_modules`
1. Run `npx lerna@5 bootstrap --include-dependencies --scope @ionic/core
--ignore-scripts -- --legacy-peer-deps && npm run build`
1. ✅ Verify: build is successful
1. Run `git revert 76cf4bda6a`
1. Run `npx lerna@5 bootstrap --include-dependencies --scope @ionic/core
--ignore-scripts -- --legacy-peer-deps && npm run build`
1. 🛑 Verify: the following error occurs:
    ```bash
[ ERROR ] TypeScript:
node_modules/@axe-core/playwright/dist/index.d.ts:2:22
              Cannot find module 'playwright-core' or its corresponding
              type declarations.

L1: import { SerialFrameSelector, RunOptions, AxeResults } from
'axe-core';
          L2:  import { Page } from 'playwright-core';

    [00:58.9]  build failed in 6.36 s
    ```

⚠️ Please do not push the reverted commit, it is just to show that the
new dev dependency is required.

This shows that without `playwright-core` installed the lerna command in
the release process will fail.

---------

Co-authored-by: Brandy Smith <6577830+brandyscarney@users.noreply.github.com>

core/package.json

@@ -65,6 +65,7 @@
     "fs-extra": "^9.0.1",
     "jest": "^29.7.0",
     "jest-cli": "^29.7.0",
+    "playwright-core": "^1.56.1",
     "prettier": "^2.6.1",
     "rollup": "^2.26.4",
     "sass": "^1.33.0",