> Will they end the system that empowered them once in power?
This is one of a couple of points where the lack of a precise definition causes the perspective to fall apart. Liberals would do exactly that by instituting democratic liberalism in a country after coming to power.
Changing a system isn't fascistic. Even replacing isn't characteristic of fascism (although what is beyond self-identification), the French are up to Republic #5 and republics generally aren't fascist. It is necessary to evaluate the change and impacts of the change in context to work out what the nature of a political thing is.
Fascists may participate in a peaceful transition of power in order to gain power, then do not allow for peaceful transitions of power in the future. Jan 6 was an unsuccessful attempt to prevent the peaceful transition of power. Just like the Beer Hall Putsch. Unsuccessful, but totally unambiguous.
Yes, obviously, changing a system isn’t fascism.
Doing so in a way that prevents any other future system change or peaceful transfer of political change is Fascism.
How is this even complicated?
We all come up with rules. Everyone follows the rules. We can all decide to change the rules, but again everybody decides what those rules are, and those rules allow for future changing of rules and actively support the peaceful transition of power. Sometimes there’s somebody who says rules don’t apply to me and I’m the only person who gets to make the rules forever and if you disagree with me I’ll kill you. One activity is not fascist, the other is.
The difficulty is fascists never say they are fascists. they don’t advertise it. They will swear up and down that they’re following the rules, and will abide by the rules right up until they’re powerful enough, that they can just kill everyone who opposes them.
> Doing so in a way that prevents any other future system change or peaceful transfer of political change is Fascism.
Instituting a monarchy isn't fascism, so that definition doesn't work either. Dictatorships aren't automatically fascism; communism for example was explicitly in opposition to fascism. The fascists in fact inflicted huge casualties on the communists despite both ideologies being authoritarian dictatorships. You're running in to the major problem in defining fascism - if a group of people don't say "we are fascists!" then there isn't anything unique that identifies the fascists.
> The difficulty is fascists never say they are fascists. they don’t advertise it.
I swear I drafted my comment before I got to this part. That is literally the only way of identifying fascism. It is a self-identification. It is like being part of a club - the only way of knowing who is in the club is talking to the people/club management. Or if they otherwise identify themselves with a funny hat or something. They didn't actually stand for any particularly clear cut ideologies.