While the similarities to anime-like magic systems (specifically HxH) are very obvious, I do like it and I feel it can be differentiated from the anime systems you likely (maybe not) were influenced by.

Please keep in mind this is all subjective. I will comment on each gate:

GATE OF AWAKENING: What I like most just happen to be the two things that seperate this from basic/advanced nen techniques, which are the linking of 2 individuals and ABSORPTION.

GATE OF REALIZATION: I like almost everything here and that the abilities arent chosen consciously.

Gate of acceptance: I say delete it. Doing so will simplify things nicely, as there is already a lot of components to play around with in your magic system. Removing it would also make fights more dependant on wit and ones capability of psychologically assessing their opponent, rather than some internal discovery thing that is basically fully dependant on when you (the writer) want it to manifest. In most cases that I've seen in anime and books where a similar component is an aspect of the world, it is usually used in a dues ex machina way to shift the tides of a battle. You can stick the 'tackle their traumas / coming to terms with who they are' to something else like the Gate of realization, or just character development.

Keep it up!