ci(e2e): cache Playwright browser install for the nightly workflow

[NotThatKindOfDrLiz]

PR #173 runs npx playwright install --with-deps chromium on every execution.

Follow-up:

• evaluate caching the Playwright browser install keyed by the relevant e2e package inputs
• keep it only if the runtime savings justify the added YAML/cache complexity

This is a non-blocking optimization.

[sergey3bv]

Hey, @NotThatKindOfDrLiz, I opened a PR to solve the issue, could you please take a look?

cc @dcadenas