perf(e2e): improve node_modules, Playwright and wp-env home caching

[Hug0-Drelon]

What?

Improve e2e CI caching for node_modules, Playwright browsers, and the wp-env home directory (downloaded WordPress sources).

Why?

More reliable cache keys and reuse of wp-env downloads reduce CI time without relying on a Docker image tarball (restore + docker load was slower than it helped).

How?

• Add a Get Node.js version step and include package.json in the node_modules cache key.
• Resolve @playwright/test version via bin/get-playwright-version.js (from consumer cwd) and add Playwright restore-keys.
• Skip npm install --package-lock-only when package-lock.json already exists; use npm ci when a lockfile is present.
• Pin WP_ENV_HOME, cache that directory, and on cache hit delete wp-env-cache.json so wp-env re-runs wp core install against fresh MySQL volumes while keeping downloaded sources.
• Drop the previous wp-env Docker image tar cache.
• Optional wp-env-cache-key input for consumers whose env content is not fully reflected in .wp-env.json (e.g. WooCommerce version / Polylang Pro SHA).

Depends on the inputs PR (e2e-action-inputs); retarget to main after that merges.
Split from #17 (cache only).

Test plan

• Cold cache: wp-env home miss → start + tests pass; cache is saved.
• Warm cache: home hit → wp-env-cache.json removed → start reconfigures → tests pass (REST API / global setup OK).
• Change package.json / lockfile and confirm node_modules cache misses.
• Confirm Playwright binaries restore via exact key or restore-keys.
• Confirm wp-env home cache key changes when .wp-env.json, WP latest, @wordpress/env version, or wp-env-cache-key changes.
• With a committed package-lock.json, confirm lockfile generation is skipped.

[Hug0-Drelon]

This PR was merged into the wrong base (e2e-action-inputs). That merge was reverted on the inputs branch; the cache work is reopened against main in a follow-up PR (cache-only, independent of #19).