I think with BL, it's a genre it's best to choose if the main plot is a mlm Romance. Think of it like the "Romance" genre, but with a gay relationship. That's kind of why it was added to Tapas in the first place; the Romance section was dominated by BL stories and creators and readers of het felt drowned out, and BL creators felt the need to write "BL" on their thumbnails so people looking for it could find it... basically it was best for everyone to give it its own category. Being the main plot means that the core conflict the story revolves around is the relationship, whether it'll happen and whether it works, and there's generally a happy ending where the two end up together (because Romeo and Juliet is not a Romance story, it's a Tragedy).
LGBTQ+ is the category for stories where there are queer themes (like coming out, transitioning, gender fluidity, asexuals finding their place in a world built around the assumption of romantic and sexual pairings etc.) Or which feature one or more relationships that aren't cisgender and heterosexual in nature, but it's not necessarily the focus of the story. The main plot it all revolves around might be more action, comedy or drama, or perhaps the story has a bittersweet or tragic ending.
Some people also describe it as "the tag to put on your comic to scare off people who won't like it if your action/fantasy/drama story suddenly gets really gay or a character is revealed to have been trans the whole time."
To me, since your story's main plot is about egg smuggling, it seems more like it'd be LGBTQ+ than BL, but it's your judgement to make.
Then the comedy vs crime thing... I'd say that dark comedy is still comedy. The premise of your story, about smuggling eggs, is inherently ridiculous and comedic, so even if it involves criminality and touches on dark themes, I don't see a reason to remove the comedy tag from it. The art style and absurd story concept will probably attract more people in comedy than in a category like mystery or crime, I think.