how to check if a windows server applied EDR EAP?

The health state for the item you reference (Sophos EDR Agent) is for the sspedr.exe process which is launched by the SSPService.exe process, which is the "Sophos System Protection Service".

"C:\Program Files (x86)\Sophos\Health\SophosHealth.exe" - "Sophos Health Service", maintains the state in the registry here for that process:

HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Sophos\Health\ProcessNotification\Sophos EDR Agent
IsRunning = 1 | 0

The sspedr.exe process is responsible for composing the trickle feed data from the journal data.

Another check would be:

HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Sophos Endpoint Defense\EventJournal\Features\EDR
Enable = 1

This shows that the SophosED.sys driver is capturing journal data for the EDR feature.

These would be evidence that EDR is enabled.

This is not possible to check this on all computers manually.

What makes you think it is not installed. You could use LiveQuery to check the keys and create a report.

If the client should have edr then health is doing the checking and it would be red due to missing services if there was an issue.

What makes you think it is not installed. You could use LiveQuery to check the keys and create a report.

If the client should have edr then health is doing the checking and it would be red due to missing services if there was an issue.