ci(e2e): cache playwright browser install in nightly workflow

[sergey3bv]

Summary

• Adding Playwright browser caching to GitHub workflow using action/cache@v4.

Avoid naming corporate partners, customers, or other sensitive external brands in this PR title or body. Use generic descriptors unless a maintainer explicitly approves the public reference.

Motivation

• A follow-up for ci: run Playwright e2e OAuth security suite in GitHub checks #173

Related Issue

• Closes ci(e2e): cache Playwright browser install for the nightly workflow #176

Testing

• cargo test --workspace --verbose
• cargo clippy --workspace --all-targets --all-features -- -D warnings -A deprecated
• cargo fmt --all -- --check
• Manual verification completed

Visuals

• UI/web change with screenshots/video attached
• No visual change
• Visuals and text avoid sensitive external brand or partner names unless explicitly approved