Currently there is no possibility to handle a background task on a page which is based on on table with scope onprem (i.e. Extension Management)

many other things can be done through eventsubscribers in a codeunit. we can even enqueue a page background task in the OnOpenPageEvent but can not respond on Task completion or error.

To fix this i recommend to introduce new generic events:

[EventSubscriber(ObjectType::Page, Page::"Extension Management", OnPageBackgroundTaskCompletedEvent, '', false, false)]

local procedure OnPageBackgroundTaskError(TaskId: Integer; ErrorCode: Text; ErrorText: Text; ErrorCallStack: Text; var IsHandled: Boolean)

[EventSubscriber(ObjectType::Page, Page::"Extension Management", OnPageBackgroundTaskErrorEvent, '', false, false)]

local procedure trigger OnPageBackgroundTaskCompleted(TaskId: Integer; Results: Dictionary of [Text, Text])