Looks like the 'Collaborate' button on any report/dashboard does not allow me to post anything to the chatter. I must be me missing some kind of permission/setting here. The feed tracking on reports/dashboards is enabled. So when there is a change to any of the fields enabled for feed tracking, the changes do appear here. But I wanted to post something using the POST action on chatter publisher. However, the POST action seems to not appear here. Not sure how to bring the chatter publisher with POST, POLL, QUESTIONS on the report/dashboard collaborate button. Please refer to the below screen shot.
I did find a solution finally. I have added the required chatter quick actions to the Global Publisher layout from setup. However, I am kind of confused here because I had to add the 'Quick Actions' to the Classic experience to see them on the reports/dashboards viewed in lightning experience. I thought 'Mobile & Lightning Experience' actions would decide the actions visible in LEX. Anyways, marking this as best answer so that it would be useful for someone in future.