I'm not sure I've ever worn a pair of pants that didn't do that. That's just something pants do. To the point that nobody is going to see that and think you've got a boner. (Unless you do, of course, but even then probably only if you're in a position that wouldn't ordinarily produce that wrinkle/bulge or your boner is visible in a different spot than that wrinkle/bulge or something.) I wouldn't worry about it. Even if you do some fancy tailoring to address it, I think what you'll end up with will look worse than it would if you did nothing.

I think that's what happens when you wear pants too big for you - the extra material has to go somewhere.

I know it's not intuitive, but taking in the waist - actually reducing the waist instead of just cinching it with a belt - can help with crotch bulge. You take it in in the back, so that the front is pulled tighter and lays flatter; some excess material is removed, and the rest gets bunched up in the back where it's not as noticeable.

https://www.wikihow.com/Make-Your-Jeans-Tighter

I'd suggest practicing on a pair of jeans you don't really mind putting holes in first - I totally screwed up the first time I tried 😆

Don't worry about it. No one cares about your pants.

Sounds like the zipper is too long - a friend was just telling me about this pitfall since I'm planning to make a pair of pants soon.

I don't have any first-hand experience, but this YouTube channel has some great videos about tailoring jeans. Not exactly your problem, but might at least help you understand the construction - https://youtu.be/AiYmCpDKmqk

This may also help - https://youtu.be/RBN10DxjW14

Take a cold shower and stop blaming your pants.