Our main site is moderated by moderators. Since some of them are busy and some are not active in moderation.
Is there any higher authority that generally responds on serious issues? If yes, what are the ways to contact them on potential issues?
Yes! They are called Community Managers.
You can check list of all community managers in this meta answer: Who is on the Community Management Team, and what do they do?
Useful meta post to learn more about CMs: Employee profiles are now marked with a “Staff” indicator
Note: Expect delay in response because currently there is shortage of staffs and hence they are hiring: https://stackoverflow.com/company/work-here/2351469?gh_jid=2351469