In Moodle, Groups and Groupings are disabled by default for External tool activity.
1. What is the reason the Groups are disabled for this activity?
2. Do I need to enable them by updating the lti_supports() function?
Groups were never implemented because External Tool does not have a local grading interface or a way to separate content by groups within Moodle. It's possible that the Tool Consumer (in Moodle) could pass the group to the Tool Provider by way of an LIS Group, so that the Tool Provider could decide how to display the information based upon user groups. However, that feature has not yet been requested.
Passing group information to the LTI tool sounds like a sensible suggestion. (Does LTI cope with Moodle's ability to put a user in multiple groups?)
Also, I forget, but does 'External tool' have any reporting features these days? If so, it is important (e.g. data protection legislation) for those reports to support separate groups mode (imagine a case where non-editing teachers don't have 'access all groups' and can access those reports).
If it helps I can create tracker issues for those two requests, but it might be better if they were done by someone who is more up-to-date than me on on LTI2, and the Moodle add-on.
LTI does have a way of handling groups, and that's through the Memberships service with groups.
A discussion about getting groups from the Tool Consumer (Moodle) to a Tool Provider is here, but seems to have stalled a bit: https://tracker.moodle.org/browse/MDL-41724