Presidential offices and ministries are both part of the executive branch of governments, though. Ministries are primarily there to organize the executive’s work, so while removing ministries will affect that, it won’t affect the separation of powers (like, say, the removal of responsibilities from a court or a chamber of parliament would).
That absolutely doesn’t mean that the power to create or disband ministries has to rest with the executive branch.
In fact, it can easily be argued that creating the framework in which the executive branch operates is the domain of the legislative branch - so the creation, merging, splitting or disbanding of ministries should also be a power of the legislative branch.
Or you could argue that it should be a power that should be shared between an administration and parliament, where an administration could introduce a motion to change ministries to parliament, and parliament would have to vote on it.
Lots of possibilities.