But is the current president separated from power?
No, he needs some power, e.g the power to veto laws.
The claim is the current president is a Fidesz supporter, rather than an independent onlooker ensuring democratic process.
To a certain extend this is certainly right, but nobody is fully impartial. But he could have proven himself and with the 2/3 majority, there was always the opportunity to end his term. Now there is the precedent that political opponents should be removed if possible.
As if that would be the only influence, by the US and by other countries.
If we had free media and educated people, influence couldn't do harm. The best day to start educating everybody has long gone, but the second best moment to start is now.
E.g. Merz could use his officially not existing influence on a public TV channel to not self-censor critical material. https://feddit.org/post/32732388