O que significa The manga is taking a decidedly different approach from what is happening in the anime building up to a tournament that was placed on an indefinite hiatus thanks to health issues concerning Akutami. ?

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" The manga is taking a decidedly different approach "
"Decidedly" here means "very clearly." The anime was probably forced to make different decisions about how to progress the story due to different time constraints.

"from what is happening in the anime, building up to"
There should be a comma here that would make the sentence more clear. "Building up to" here means "getting ready for," or "setting the stage for." Making the necessary preparations for the next part of the story to make sense.

" indefinite hiatus "
A hiatus is basically a break, or pause. "Indefinite" means there is no set length of time; it could be a short time or a long time.

" thanks to health issues concerning Akutami "
Assuming Akutami is the author, he probably had to take a break from drawing the manga to take care of his health.

Overall what this paragraph seems to be saying is:
"The manga is preparing for a tournament arc which was put on hold due to the author's health issues. The anime didn't do this."

However, the sentence is constructed poorly, so what they really might have meant was:
"The anime is taking time to build up to the planned tournament arc because the manga was put on hiatus."

Without having watched the anime and read the manga, it's not clear which meaning is correct.