The external tool no longer appears to have the complete common module settings including group mode, groupings.
Hm, you are quite right. I don't see Groups here at all in any version since 2.9 up to current 3.4.
I suspect this absence is due to the potential collision of Moodle groups and LIS Groups, which are an LTI feature.
Support for LIS Group variables was added into 3.4 https://tracker.moodle.org/browse/MDL-55358 so that the course groups would pass over into groups on the provider app side, if it supported them and requested them.
So basically, if your LTI is configured to use groups in some way then it will send them; if not, it will not. The app decides this and there is probably some configuration setting for this or a url parameter to pass, or whatever.
I have not used a group aware LTI app yet but the issue to me would be how you designate which groups to use. Since a course may have many groups and groupings and users may be members of multiple groups which have no relation to what the LTI activity does, there would need to be a way to do that.
So, for Turnitin, you would need to ask them if they support groups at all and if so, how that is set up on your side.
You can still use the Groups/Groupings for the Access restrictions, but that is a different thing. Useful but different.