My question: Which of these builds is best optimized for damage?
I am wondering about the amount max average damage each of my suggested builds could put out each turn. This seems like a math question, I am confused to why it is too broad.
Also why is this question not too broad: Optimizing a dual-wielding ronin blademaster
I think your question is too broad it is because you're asking too many things at once, and haven't defined it in a way to have a singular meaningful, useful answer.
You're asking what the optimized damage for three different builds are. On top of that, you're asking for average DPR as well as maximum single turn damage (which I assume you mean this by single-use). That's six answers with unique calculations bundled into a single question. Seven if you are still asking 'which of these is the highest number', but that's moot once you have the data in front of you.
This also presents a problem since you want it Adventurers League compatible. In my experience, AL rewards magic items intermittently and restricts access to many magic items, and giving you an optimized build assuming free access to all items isn't going to be a realistic scenario for your character's progression through AL. Many builds rely on specific combinations of magic items to either offset weaknesses or amplify strengths.
This differs from the question you linked because that question gives very clear constraints, and a solid character concept that we can build around. "Dual-wielding martial ronin" is much more specific conceptually and thematically than what you provided.
It's worth noting that, when your question was closed, it was lacking a lot of detail. "Why was it closed" is not the same as "can it be reopened". I can't say for certain why your question was closed, as I was not one of the users that voted to close it. The listed close reason usually isn't too informative, so I'll recommend not focusing too much on the "too broad" part.
I can, however, offer a few observations that have kept me from voting to re-open the question as currently written, even with the substantial edits that have already been added:
It's not clear to me that there is a whole lot of question in it. There are three builds, with all class levels and most class specializations already chosen. It's not totally clear to me which variables still exist within each build. If there are few to no choices to make, then calculating maximum and average per-turn damage is a pretty straightforward computation, more suitable for a calculator than RPG.SE. That's not fatal to a question, but it strongly suggests that as part of your basic research effort (an expectation on all questions) you would present your own calculations for each.
It asks a somewhat oddly structured question. Optimization questions usually state a goal and some starting constraints, along the lines of
I'm creating a character that will have X levels in Rogue, choosing the Arcane Trickster specialization, and Two Weapon Fighting (Fighter or Ranger). With those constraints in mind, how can I build a character optimized for damage at level 20? I'm interested in both the highest single-attack damage and also the highest average reliable damage.
In contrast, this question includes three nearly complete builds (with respect to dealing damage), asks an optimization question for each of them implicitly, and then asks for a straightforward comparison of each of those. Additionally, because each of the builds has the same "base", it's unclear to me why they need to be considered at all. As above, a question asking about an optimized damage build with 15 levels of Rogue, taking the Arcane Trickster specialization, and Two Weapon Fighting (from Fighter or Ranger) seems like it would answer your question. Imposing the three builds seems to me like it distracts from what you are hoping to learn.
The question includes vague considerations that I don't understand in the context of writing an answer. The second build listed seeks "more versatility". If this is a damage optimization question, answerers will have trouble incorporating and understanding other factors unless you define some kind of hierarchy illustrating what tradeoffs you care about most. Similarly, from how the builds are written out I'm not clear on how those Attribute points were assigned, if there are ASIs available from advancing class levels, and so on.
So, in summary, the question is a little bit unclear about what constraints exist, what options exist, and what specific information you're seeking but don't already have. This is then tripled, for reasons which also seem a bit fuzzy. Those aren't necessarily enough to cause it to be closed, were it a fresh question, but that's not the situation we're in. These are reasons why I'm a bit hesitant to vote to reopen it myself, though other users may feel differently.
The other question:
Even if another question "should have been" closed as too broad, that doesn't mean anything with regard to your question. If they should both have been closed, the correct response would be to close the other one, not to open your own.
The other question contains a lot of detail about what the OP wants to achieve, in terms of both flavor and mechanics. It also lays out which class levels are required for the optimized build, and which are open for change. It includes priorities, and therefore tradeoffs, and a lot of detail about how the character is intended to be played.
It's also worth noting that that question was not that much better received than yours:
