The Synthetic Classic Portal displays the true status of the test: if the Portal says it's active, the test is actively running and collecting data.
When you use the Open (remote) command in Windows Recorder to edit a script that's been uploaded to the Synthetic Classic Portal, the Recorder gets information from the scripting database, which stores the script status.
For Last Mile*, the script id is different as the test id thus script status does not reflect the test status; this is different as Backbone, that script id is the same for test id thus script status is the same for Backbone test status.
This is also related to a known limitation that, for Last Mile*, scripts associated with tests that have ever been active are listed as active permanently, even if their associated test is now inactive.
For purposes of data collection through APIs and billing, the Batch Order status in the Dynatrace Classic Portal is the true status of the Last Mile test.
* This is the same for Last Mile, Private Last Mile and Mobile tests.