so the scouts would be more like the cia. that analogy would bring just about everything into focus.
Possibly a bit more like how the US Coastguard comes under the Department of Homeland Security.
One definition of the tasks of a police force is: "to know where everyone is at any given time".
Scouts have a massive passive intelligence gathering capability in the form of detached scouts. The SSB act "as clandestine agents for Intelligence Branch".
So when a suspect needs arresting the Scout Service are likely to know where that person is and can send a team with the right skills to take that person into custody. Of course the above may equally apply to suspects or persons of interest outside the Imperium (so a bit CIA-like). Besides people, this may also apply to seizure and retrieval of things (like technology on an interdicted world).
Scouts "also have extensive law-enforcement powers among the general public. They may question, detain, or arrest suspects for violations of many Imperial laws. In particular, they hold the primary responsibility for enforcing the interdiction laws with regard to worlds which are under IISS jurisdiction."
Extensive law-enforcement powers may mean they can intervene in any crime against the Imperium they encounter, but in practice they probably stick to things they know about like breaking interdictions.
The other emphasis is on internal security and policing. The Scouts are a big organisation with lots of property, like ships and bases. So guarding those, checking out employees and keeping them safe are all tasks of the security branch.
Both the above are backed up from CT Scouts and GT First In. I'd assume one more big area for the Security Branch is investigating crimes that use the X-Boat network. That could be literally any crime, so I'd narrow it down, let the Imperial Treasury investigate financial crimes and currancy fraud, local customs can probably deal with transmission of offensive or illegal materials but things like treasonous materials or communications might first drop on to the desk of a SSB operative.