With Moodle as LTI tool (provider) in control of the LMS's gradebook, currently all activities remain "Not Started" in the LMS (platform), even though the learner has opened them, as Moodle will only send any outcome back upon course completion:
https://github.com/moodle/moodle/blob/a52fbcced680f44f7ac41c25b8bf80a5bbe56fb3/enrol/lti/classes/local/ltiadvantage/task/sync_tool_grades.php#L164

Ideally \ltiadvantage\task\sync_grades would also send intermediairy outcomes; e.g. "Started" when a student has started the activity, and "Submitted" when the student has submitted it for marking by the teacher.

See https://www.imsglobal.org/spec/lti-ags/v2p0#activityprogress