want to get access to the site admin’s email and send an error message to the mailbox. According to my knowledge, I can get the network. But how can I get the same in APEX?

Apex site administration may not be very flexible when it comes to giving away some information. To understand how to get information about the community site administrators in APEX, you first need to figure out how the community administrator is defined. Read about it thoroughly if possible. You can use the NetworkMember object to find the information as well. This can solve the issue. But in case this does not solve the problem, you can try to use the network for the community and profile for the admins present in the same community to find out the required information. It can help to understand who is part of that community.