ci: backport GitHub Actions maintenance to v1.x

[mstoykov]

What?

Backport selected GitHub Actions and workflow maintenance updates to v1.x.

• Update pinned action versions and Vault secret handling.
• Run CI workflows on pushes to v1.x.
• Fix the browser E2E branch trigger and disable its Go cache.
• Skip code-heavy workflows for docs-only and release-notes-only PRs.
• Move test coverage to Ubuntu 24.04 and install Chromium consistently.

Why?

Keep the maintenance branch CI current and reliable, ensure workflows run on v1.x, reduce unnecessary CI, and preserve release packaging compatibility.

Checklist

• I have performed a self-review of my code.
• I have commented on my code, particularly in hard-to-understand areas.
• I have added tests for my changes.
• I have run linter and tests locally (make check) and all pass.

Checklist: Documentation (only for k6 maintainers and if relevant)

• I have added the correct milestone and labels to the PR.
• I have updated the release notes: not applicable
• I have updated or added an issue to the k6 documentation: not applicable
• I have updated or added an issue to the TypeScript definitions: not applicable

Related PR(s)/Issue(s)