ci: fix playwright install

[hi-ogawa]

Description

It looks like pnpx (equivalent to pnpm dlx) is downloading a latest playwright version which doesn't match with the ones listed in Vitest monorepo dependencies.

It seems pnpx is considered deprecated (see https://stackoverflow.com/a/70266473), so I replaced with a explicit variant of pnpm exec, which always uses locally installed version of cli.

For pnpm exec playwright ... to work at the root, the dependency needs to be at the root, so I moved the one from test/ui/package.json to the root package.json.

Please don't delete this checklist! Before submitting the PR, please make sure you do the following:

• It's really useful if your PR references an issue where it is discussed ahead of time. If the feature is substantial or introduces breaking changes without a discussion, PR might be closed.
• Ideally, include a test that fails without this PR but passes with it.
• Please, don't make changes to pnpm-lock.yaml unless you introduce a new test example.

Tests

• Run the tests with pnpm test:ci.

Documentation

• If you introduce new functionality, document it. You can run documentation with pnpm run docs command.

Changesets

• Changes in changelog are generated from PR name. Please, make sure that it explains your changes in an understandable manner. Please, prefix changeset messages with feat:, fix:, perf:, docs:, or chore:.

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