Staff management (i.e line management) which would include sickness management (return to work, attendance at work, welfare calls), general performance (1:1s, devlopment) and formal processes (discipline, grievances, complaints etc.).
Administrative work, such as assisting rostering (more if no dedicated roster clerk) and coverage issues and shifting people around as required. You might be asked to get involved in supporting encourage people to do rest day work. Ensuring compliance with various processes and procedures. Probably will get involved with all elements of the company from uniforms to IT!
There will likely be service quality work too - e.g. how tidy is the station, how presentable are the staff, are the information displays accurate etc.
You'll no doubt have various initatives to be involved with as the company sees fit. You will likely be expected to support during events and disruption as well to provide a management presence "on the ground". You might have some on-call responsibilities
As you say there's no "typical day" nor one size fits all; you could be one of several managers at a big terminus, the sole manager at one large station, or manage a bunch of smaller 'line of route' stations with various levels of supervisors to support the day-to-day. Very much a "jack of all trades" role.