That also might depend on what type of methodology you workin in.
in scrum were making separated tasks for e2e tests in our stories, so it was pretty easy to see what's done.
e2e tasks were picked up when UI was done, we also agreed that delivering feature with e2e tests in the same sprint (like 2 weeks period) is difficult, and Automation QA work was some sort of detached form what devs were doing so e2e tests were never included in the spirt goal.
We were just making sure everything is covered with regression tests before important releases