I am more used to the old fashion Target way of providing guest service.  I can't really comment on too much about the modernization process.
Sometimes you just have to bite it and entertain your TLs and management.  A new GSTL is just trying to get things established and learn the ropes so they have to go by the book.
But a GSA moving a couple carts while on their 15 is one thing.  If they make an excess effort of moving carts, then may need a unofficial coaching.  Moving carts on their lunch while off the clock is a big NO.
When you engaged and assisted the guest, did it require you to step away from the lanes?  As a cashier, you need to stay in sight of the lanes.  But forward the guest request to the GSTL/GSA on duty so they can communicate the request to the floor.  Never go rogue and walk away even to help a guest.
As being global on the front, I covered all areas for the front.  GSTLs were comfortable with me identifying when additional assistance for SD or FA was needed.   I would be working carts.  But I would cashier/SD until carts were needed.  If the SD line was long, and their was enough coverage on the lanes, I would jump off to help them.
If anything, communicate to this GSTL and ETL where communication and performance could be better explained.