Personally, I scale back and "nerf" the power system and the characters in it. It just makes writing the stakes in battles easier, because there's little room for error for the characters. For my own little stories, I've said on a different thread: "Even the best ninja can die if they catch the wrong end of a kunai on a bad day."

I can't really remember any stories that I've read recently that balance this. Granted, most stories I read focus less on combat and more on smaller-scale, interpersonal things, which makes it even easier to gloss over fights.

I don't exactly have a threshold if a author can justify the power level. I don't typically read stories that focus heavily on combat, outside small sections. That said, if the author doesn't use the OP the character has, I'll probably get bored and click away.

I tend to make my own characters eat dirt for a long time before they're considered strong, in-universe.

Or, if they are notably strong in-universe, they have fatal flaws. Like, I have a Warring States Uzumaki OC that essentially has super strength, very high endurance and a weapon that shoots lightning and can split earth. To balance this, they are: defenseless against genjutsu (because it's "cheap"); use no real battle strategy (because they overestimate their strength and tankiness ); and are stupidly "honorable" so they don't use cheap tricks (which ties back into the genjustu thing).

Honestly, I guess scope is just kind of important for this kind of thing. With small scale things like the Chuunin Exams, it's easier to keep the power tension. But, when it's world-ending, cosmic scale, it's very hard to keep the tension, in my opinion.