According to the docs there's a limit to how long can background execution be used (ExtendedExecutionSession). However, it also seems that some of that page refers exclusively to mobile.
Is there a limit to how long it can run on desktop?
The docs you linked cover desktop scenarios as well as mobile. Search for "desktop" and you'll find information such as:
On desktop devices, extended execution sessions created with ExtendedExecutionReason.Unspecified have a battery-aware time limit. If the device is connected to wall power, there is no limit to the length of the extended execution time period. If the device is on battery power, the extended execution time period can run up to ten minutes in the background.
The user can choose to ignore the battery limitation on an app-by-app basis.