Security capitalization

Nope.

You'll need to notify security if you want to work late in the office.

https://dictionary.cambridge.org/dictionary/english/security

Also:

security department - a department responsible for the security of the institution's property and workers; "the head of security was a former policeman"

https://www.thefreedictionary.com/security+department

If the security department has the (well-known) name Security Department or Security then capitalising Security would be fine. Otherwise, I don't see why you would need to consider it, given the above. The word security is the general term for any such departments/staff/etc.

I would say yes, as security feels to general, whereas as you said, Security would highlight that it's a specific department, with a name.

In general the rule is that capitalize a word if it is a name. If the group that does the throwing has the name "Security" then capitalize.

Here it seems likely the people speaking don't know the formal name of the group, so it is not possible to make a definite decision. But capitalizing has the advantage that there is no possible confusion with other meanings of the noun "security".