What Scrum Master should do full day?

Debate whether reporting is part of the SM tasks?

On a serious note; helping the team(s) and organization to focus and improve on inspect, adapt and transparency...

maybe this will help maximizing the SM value: https://www.scrum.org/resources/blog/8-stances-scrum-master

If I'm busy all day, then I tend not to be an effective Scrum Master, because I don't have time to see what's going on, or step in when it's needed.

Most of my time is spent being ready to act when it's needed.

I try to keep gaps in my calendar, so team members or other colleagues can ask me questions, or come to me for help.

I have chosen to take on other activities, but a good Scrum Master needs to work out what is helpful in their situation. For example, I have 1:1s with all members of the Product-Engineering team, and a couple of other colleagues.

I look for patterns in the metrics so I can ask questions to help the teams learn, and challenge assertions that are made solely on gut feeling.

I also tend to sit in on various other meetings, so I can have as much context as possible about the various initiatives being taken by Product Owners and engineers.

I have regular meetings with my manager, so I have context about what the leadership team are trying to do, and I give him feedback about what impact his and the leadership's actions are having on the teams.

@Simon - If SM is a technical person, he can spend some time to assist the team in technical queries. But what to do if SM is not exactly from the technical background?

This is one of the reason I noticed in several teams which makes them think that SM wont be able to help them or will not be able to remove their impediments.

How to deal with this situation?

I have a technical background, but I try not to use those skills to assist with technical queries. I'm more focused on making sure the team are able to answer those queries by themselves, or even getting into a position that no-one needs to ask such technical questions, because the product just works intuitively.

How to deal with this situation?

My approach tends to be that I'd probably provide transparency of the problem, I'd coach the person to be able to escalate impediments to someone who can help and/or I'd get people in the same room (or video call) to talk about what's going on.

If that doesn't lead to the impediment being resolved, I would probably keep asking questions until the underlying problem emerges (e.g. maybe no-one has the required skills, or different teams have competing priorities, or everyone is overworked). Then I would repeat the process with whoever could address that underlying problem.

But that's just one theoretical way of responding. Impediments are usually complex problems to be solved. The skill of a Scrum Master is finding the right response at the right time. In my experience, clearing the impediment directly is rarely the best option. It usually hides underlying problems, and denies the team an opportunity to learn and grow.

In addition to some of the other answers, back when I was in the office on a regular basis, I would perform a Gemba Walk. The concept comes from Toyota, where the executives and managers would walk around the manufacturing floor and see, with their own eyes, the work that was happening, what problems were coming up, and look for wastes or opportunities to help the folks doing the hands-on work improve.

In my experiences, there are plenty of things that don't come up in Daily Scrums or Retrospectives. They are very small, minor things. Walking around and talking to people, either at their desks or going to the watercooler or coffee machine and talking to people to understand the things going on can generate improvement opportunities. Some are "just do it" type of things, while others make good discussion points in the Retrospective and I can jog the team's memory. It's also a good opportunity to just get to know the people who are working with you and build relationships and trust.

Unfortunately, I haven't found a remote equivalent of this yet.

But what to do if SM is not exactly from the technical background?

Do you need a technical background to recognize empirical process control, and to recognize when constraints impede it and when to take action?

Scrum Masters should also work on creating new workshops to build team spirit, collaboration and teaching people about the benefits of business agility. The Scrum Master can also work on exploring new tools for gathering customer feedback, or measuring success, and advising the Product Owner on those new methods or tools.

No Agenda and visualizing business value with PO might be an approach to drive development team to achieve them rather than just delivering work

Once done with the ceremonies and reporting tasks

I would challenge this thought and ask, by doing this, how does a Scrum Master support self-organization? I don't disagree that the SM should facilitate events (as needed), however, that is not the only thing a SM is supposed to do.

what all are the tasks a scrum master can work upon? as SM don't work on actual deliverable of the project.

Scrum does not restrict a SM from executing work in the Sprint Backlog i.e. if they have the technical skills they can contribute. It just needs to be made transparent how this may impact the responsibilities when one person assumes both the roles.

The SM has service not only to the DT, but also to the PO and to the wider organization, therefore the SM could be involved in activities like training, workshops, facilitating communities of practice, interacting with leadership, finding ways to remove existing impediments etc.

Hope that helps.