My understanding is that you want a word for "power" that applies to both the ability to materialize/ manifest/ conjure/ generate/ summon/ annihilate or reify/ concretize through a performative utterance, or prestidigitation, as well as the word for something that is in your purview.
Based on your follow-up comments, it seems like you want a word that isn't too strong (dominion/sovereignty are too strong to use), so I think part of the challenge is to find a word that's not too strong for purview but strong enough for prestidigitation. To resolve this, I'm thinking of finding a word that works for the latter "purview example", that can be used metaphorically in the "prestidigitation example". (Or just use "power"! Or just use two words for each situation! Based on your clarification, I'm still not quite sure what's wrong with "power"?) You liked "reify" but that doesn't work for both examples, does it?
Words like "command, authority, governance, purview" come to mind. However, I think the word that comes closest to working for both examples is "prerogative". Pregoative can refer to a "power or immunity" that is unique to the situation you deploy the word. In other words:
Prerogative
"a right, privilege, [power,] etc. unique to a specific person or persons of a particular category"
The "power" sense of prerogative can be specific to a governance/polity, but can also be metaphorical, as in "it's your prerogative to [do something]".
I think that captures all of your stipulations: not necessarily physical power, works for magician example, not limited to one thing (such as state power), not overly general either (eg, omnipotence). The word is also "modifiable in combination with a subject to indicate a single thing or concept to which the power applies", for example, "royal prerogatives" or perhaps "existential prerogatives" (example) when referring to being about to magically being able to bring/remove something from existence. Prerogative also works for the more quotidian example of a network administrator.
refs:
https://en.wikipedia.org/wiki/Performative_utterance
https://www.dictionary.com/browse/prerogative https://www.collinsdictionary.com/dictionary/english/prerogative
https://cio.economictimes.indiatimes.com/news/corporate-news/hyperautomation-an-existential-prerogative-for-organizations/89816390?redirect=1