From all the similar 5.6 cases you've seen, have you seen any that were eventually resolved?
The only similarity is the "Developer code of conduct" violation. I'm sure each individual situation is unique.
But unfortunately, I don't recall any post regarding this guideline where there was a positive followup. I've seen many cases of individual apps being rejected on other grounds, where I thought the rejection was legitimate, but they ultimately followed up saying the app was approved.
Because if Apple can reject a legitimate business
No one is claiming your business isn't legitimate. Apple's a private company. They don't have to do business with anyone they don't want to, for whatever reason. Apple can, and will, reject apps without any stated violation of any guideline.
provide no clear explanation of what triggered it, and then leave the appeal unanswered for weeks
Unfortunately, that's typical. Again, Apple has no obligation to explain why they don't want to do business. I do this myself sometimes. When I see someone that's going to be a real problem, I just issue a quick refund and I'm done with it. I never explain why. That would be a real mess. Just cut my losses and move on. I don't fault Apple for having a similar policy.
Abandon the business because Apple won't approve the app or explain what needs to be fixed?
I'm afraid you'll have to do that review on your own. Please don't post any more details here in the forum. That usually reveals personal details that shouldn't be disclosed in public.
The "Developer code of conduct" is usually a developer account termination action. Yet you're talking about it in terms of a simple app rejection. And you've also only waited a month. Typically these issues take longer than that.
You might want to try a "Meet with Apple" session and get some clarification regarding whether this is a simple app rejection or if your entire developer account is at risk. Obviously, if you have more app rejections, then your developer account would be at risk. In the guidelines, there is a remediation process for a 5.6 violation. But I'm absolutely certain it will take longer than a month, even if successful. And to clarify, the app itself is dead. Give that up. You need to be fighting for your developer account instead.