ci: fix aur apt cache as well

[goniz]

Followup PR #13897

This PR extracts the fixes for APT cache to a reusable action and applies it to the AUR packages as well.

[github-actions]

Hey! Your PR title ci: fix aur apt cache as well doesn't follow conventional commit format.

Please update it to start with one of:

• feat: or feat(scope): new feature
• fix: or fix(scope): bug fix
• docs: or docs(scope): documentation changes
• chore: or chore(scope): maintenance tasks
• refactor: or refactor(scope): code refactoring
• test: or test(scope): adding or updating tests

Where scope is the package name (e.g., app, desktop, opencode).

See CONTRIBUTING.md for details.