Your external system once done processing has to call Salesforce and tell that process is done. One way I can see is using customNotificationAction. They also have a rest endpoint that can be called from 3rd party.
curl --include --request POST \
--header "Authorization: Authorization: Bearer 00DR...xyz" \
--header "Content-Type: application/json" \
--data '{ "inputs" :
[
{
"customNotifTypeId" : "0ML1k0000008OIFGA2",
"recipientIds" : ["0051k000001G0f5AAC"],
"title" : "Case Closed!",
"body" : "Your High Priority Case has been Closed.",
"targetId" : "5001k00000BrdQ9AAJ"
}
]
}' \
"https://gs0.salesforce.com/services/data/v46.0/actions/standard/customNotificationAction"
https://developer.salesforce.com/blogs/2019/06/get-buildspiration-with-custom-notifications-in-summer-19.html