Security checks are mostly automated. Based on biometrics and other information available, they try to trace your information across available data and the data shared between countries.
Medical is mostly handled by other visa office and are updated independently.
Background + eligibility are linked.
Medical, Security and some parts of background check are mostly go on behind the scene and require no input from visa officers. They rather just verify the data received and use that to make (or finalize) a decision.
Eligibility is done differently by different visa officers, some may just look at the documents and make decision with the information available(that also depends on the nationality of the applicant), some may request additional documents to help understand the application and make an informed decision, some may even request internally to fraud check + authenticate the documents before they finalize eligibility. More or less, every visa officer is going to go thru these steps, it's just the preference of the visa officers when they choose to do it. Some may choose to wait until Background + Authenticity of the documents (transcripts, financial documents, employment, IELTS) are all verified to complete eligibility review, while some may just conditionally pass eligibility given that the rest of the information turns up without any issues. Based on the proposed study plan, they also try to make sense of what the applicant is attempting to do based on the previous education, age, gap between education, career, family assets and future goals from SOP.
Certain countries eligibility may take a day to be completed where historically applicants provided genuine documents 99% of times while others may take from some days to weeks where historically fraud + fake documents have been used multiple times. That's where the delay comes in to authenticate, trace and eliminate any doubt regarding documents.
This is mostly my understanding of the process which is based on the numerous GCMS comments from Visa Officers.