LN version the manga is based on has been licensed by J Novel Club under the title The Magician Who Rose from Failure - Tales of War and Magic.
https://i.redd.it/yh5lkytnc4s51.png
So far that's Arc's long term plan. Last I checked he's scored a few victories of his own but otherwise he still feels it's insufficient to properly show off to his family just yet.
iirc he has not; he still feels he hasn't made the Big One just yet. But at this point the family's been ignoring him, leaving Arcs free to do as he likes.
So what did the teacher/uncle say when the mc asked him about his decreasing magic, the day after? I mean, ignore it he might do, but he is still obviously going to inquire about it, no?