chore: include playground in nx release pipeline

[lukascivil]

Objective

Move the playground deployment out of the per-push cd.yml workflow and into the release pipeline, and make playground a first-class project in nx release so it is versioned, tagged, and changelogged alongside the publishable libraries. This ties the deployed playground to a released version of json-difference instead of whatever was last merged to master.

What was done

• .github/workflows/cd.yml: removed the Build (playground) and Deploy Playground to Github Pages steps so the continuous workflow no longer deploys the playground.
• .github/workflows/release-and-publish.yml: added the GitHub Pages deploy step, gated by github.event.inputs.dry_run != 'true', so the playground is only published when a real release runs. Updated the dry_run input description to reflect that it now also skips the playground deploy.
• nx.json: added playground to release.projects so it participates in independent versioning/tagging/changelog with the other projects.
• libs/json-difference/project.json: set generatePackageJson: false on both build and build-browser targets to stop @nx/vite:build from emitting an autogenerated package.json into the output.
• libs/json-difference/vite.config.mts: replaced the nxViteTsPaths() plugin with the built-in resolve: { tsconfigPaths: true } option.
• package.json / yarn.lock: bumped the playground's json-difference dependency from pinned 1.16.1 to ^1.16.2 so it tracks patch releases of the lib.
• CLAUDE.md: updated the "Release flow" section to list playground as a released project and to note that it is private and therefore skipped by npm publish.

Test plan

• Run yarn release:dry-run and confirm playground appears in the version plan alongside json-difference and json-difference-cli.
• Trigger the release-and-publish workflow with dry_run: true and verify the GitHub Pages deploy step is skipped.
• Trigger the release-and-publish workflow without dry run (or simulate) and verify apps/playground/dist is published to the chore/gh-pages branch.
• Push a commit to master and confirm cd.yml no longer attempts to deploy the playground.
• Run yarn nx build json-difference and confirm no package.json is emitted into libs/json-difference/dist.
• Run yarn nx test json-difference and yarn nx run-many --target=type-check to confirm the vite config change did not break path resolution.