Right now I'm creating and maintaining task status in the tracking tool. It's tiring. Should this be the job of the PM or EM to do during our catch-ups?
The one who has good overview of the project / architecture of the system should make the task list.
have done this myself at almost all of my gigs. can you automate the workflow based on tags/formatting of version control events and commit msgs?
Devs have better things to do than update their task list. Just update it with them during standup.
Whoever owns the task, i.e. responsible for its outcome, should own everything related to getting it done. That may include maintaining trackers, setting up meetings when necessary, following up, etc. In a well-functioning org everyone is focused on achieving the desired outcomes, and takes full ownership of their part.
As a software engineer?
Mostly TPMs handle that