I mean, in real life, you would tell someone that they're being melodramatic when they're overreacting. I think it's the same for stories -- when a character overreacts, and emotions are too explicitly spelled out, we feel like it's melodramatic -- the situation doesn't feel real, it doesn't feel honest. People wouldn't act like this unless they were acting, trying to manipulate you.
As far as comic relief goes, personally I find that trying to INSERT FUNNY MOMENT HERE tends to go poorly, or feel a little forced at best, so I tend not to think of funny moments as "comic relief" for that reason? I don't think it's an issue of like, how much comedy you use -- you can write a good story with no comedy and you can write a good story with lots of comedy -- but more an issue of how it's implemented. Like, if a creator finishes a page or a scene, and they know it needs a good endbeat, but they're scared of being seen as overdramatic so they don't want to end on a serious, dramatic beat, and so they have a character crack a joke or make a snarky comment or do something goofy to break the tension so that they can end on a punchline, instead.... I think that can immediately feel dishonest, in a way? Like they built to a dramatic endbeat and then pulled the punch at the last minute because they were scared to follow through.
I have a lot of jokes and moments that I play for laughs in my own story, but the moments I'm happiest with are the ones where it's not me trying to invent a funny moment, but like, just being honest about who my characters are, and being willing to laugh at something I personally think is funny. I think it's okay if the tone of the moment is serious but the character is cracking jokes because they're stressed or upset. I think it's okay to laugh at the absurdity of a situation. But I think it can hurt the moment if you try to force its tone to suddenly change because you want to cram some Comic Relief in there.