
Debut or Die: https://www.mangago.zone/read-manga/debut_or_die/
The S-Classes that I Raised: https://www.mangago.zone/read-manga/the_s_classes_that_i_raised/
I think the second one fits really well. The mc isn't the typical wants to be the strongest and super op, but he's strong in his own way and has a goal that he'll stop at nothing to achieve. I also just think the story is done really well and isn't the typical dungeon story.
If you want the more classic Solo Leveling type story though, I can give you some.

lol, I wonder if you've already read the ones I'm recommending because it seems like we have similar taste
I don't read a ton of idol manhwa, but here's one: https://www.mangago.zone/read-manga/my_second_life_as_an_idol/
I'm guessing you've probably read ORV: https://www.mangago.zone/read-manga/omniscient_reader_s_viewpoint/ and TCF: https://www.mangago.zone/read-manga/trash_of_the_count_s_family/ but if not
https://www.mangago.zone/read-manga/sss_class_suicide_hunter/
https://www.mangago.zone/read-manga/return_of_the_frozen_player/
https://www.mangago.zone/read-manga/trapped_in_a_webnovel_as_a_good_for_nothing/
https://www.mangago.zone/read-manga/the_novel_s_extra_2022/
Recs where the mc wants something really bad (debuting as an idol, becoming the strongest, etc) and will do almost anything to reach that goal?? When someone tries to stop them and almost succeeds or something, they get pissed and dissolve the issue. Or if the mc is really protective over a close friend/relative. No romance plz, but I wanna read one where the mc is powerful n like what I've been describing. (๑•ㅂ•)و✧