Can a user mass update tasks?

if I recall correctly, bulk editing tasks is a Plan license functionality. (if they have plan licenses you may also need to make sure they have manage permission on their tasks)

As long as they have manage access on the tasks they want to edit (i.e. if the tasks are assigned to them or they have manage access on project), yes you can bulk select tasks and post the same update in all and change task status. Since they're across projects though, you'd need to have a task report to start with to be able to select the different tasks. When multiple tasks are selected > edit > there's a comment area at the bottom > if you make a comment there it'll post as an update in each task selected:

And in the same edit window of course there's the task status field that can be changed as well.
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