Goes further than that, imo. Toxic masculinity can also be subtle. It doesn't need to be a chest-beating guy. Besides trying to hold a death-grip on your emotions, sinking yourself into whatever society holds to be manly, I can't really think of an example rn, I've just woken up.
If a male gets grossed out by the idea of wearing pink, that's toxic masculinity. It's ok to have preferences, like I don't like the color pink" but to be actively repulsed by it shows you have a fear of being emasculated. You have a fear that you might be seen as "not a manly man"
Other examples include being repulsed by rainbows, being afraid of showing your feelings/crying, being afraid of gay people, etc.
Good thing to have are: being willing to have a discussion without trying to "win", get angry or disregard the other person's opinion. Having women friends that you aren't trying to fuck. Having hobbies that are fun, and that you're willing to talk about because they make you excited, without trying to monetize them.
Not OP, but probably realistic is a better word for it. OP mentioned nerdy, so maybe physically weak, shorter than average, etc. Basically the opposite of 6’+ gym rat with year round 6-pack.
I'd prefer if the protagonist did have other typically nerdy traits (a poor social life, an interest in technology, movies, literature etc.) but I wouldn't exactly mind a more realistic protagonist since I don't have many choices.