Anything with the yaoi genre will have (Yaoi) in the title. Mangago was a yaoi focused site to begin with, back in the day this was basically the only site you could even find yaoi works on because other manga sites avoided/prohibited it so that's probably why there's only tags for yaoi
I think it’s a mixture of your first two theories.
I’m unaware if it’s still up, but the Mangago admins originally ran a gay romance fansite that contained stories, images, and videos from a variety of mediums.
Mangago was created as an offshoot to focus on manga as a whole (primarily BL). Because the site now served a broader audience, works included (yaoi) in the title to avoid unnecessary hate comments or confusion regarding the content.
Why do yaoi works have that "(Yaoi)" parentheses at the end of their titles? It's not visible when you search for the title or see it on the homepage, but once you've clicked it, the title adds the suffix (Yaoi).
Is it to distinguish it from possible other works that have the same title that are non-yaoi genres?
Or is it like a warning that this is gonna have hardcore yaoi depiction.
Does it only appear if the genre tags 'yaoi'?
Why yaoi specifically, not yuri, or other works here in mangago?