How do I troubleshoot a problem for a registered user under certain circumstances?

[vannilla]

The title means that I can't use a certain feature of a website, but this feature can be accessed only by registered users that first used another feature of that same website.
So, rather than asking wether other people have the same problem, the thread is about what to do to troubleshoot it, because I can't expect people to register, etc. there just to check the problem.

The issue:
I'm registered to eBookJapan, which is an online retailer (officially) selling digital versions of comic books. I bought a couple of comics there.
Recently, they joined Yahoo or something like that, and with that came a new website.
In the previous website, I could access the online reader by using an user agent override, but with the new site, no matter what I do, the reader just won't open.
I tried Firefox compatibility, I tried a user agent override, I even tried Basilisk just in case, but nothing happens.
The console shows no errors or warnings. There are some debugging statements, but they appear only when I use eMatrix. On a clean profile there's nothing.
It works on Firefox though.

As you can see the problem is about the reader, which can be accessed only by registered users who bought something.
Since I'm not expecting people to buy something there just to help me with this, what can I do to solve this issue?
Where do I have to look? What should I test?
It seems the whole website is based on the Nuxt framework, for what is worth.

I'm posting in the Linux subforum because I use Linux, but it's likely to be system-independent.

[Moonchild]

How about asking ebookjapan for assistance first?

[vannilla]

How about asking ebookjapan for assistance first?

What I thought was, why does it work on Firefox and not in Pale Moon? Especially since it appears that the whole website is built on top of a framework.
Why isn't Pale Moon able to open their reader? Is it missing support for some scripting feature? Is it some particular configuration?
That's why I asked what I could try on my end to see what the problem is. If Pale Moon (or Basilisk) doesn't have anything wrong, then I will ask eBJ.

[Moonchild]

Especially since it appears that the whole website is built on top of a framework.

We can't debug or troubleshoot framework issues because we won't have any relevant information about it, the errors it throws, or even a workable js copy (since framworks tend to toss minified js to browsers in "production" mode)

Why isn't Pale Moon able to open their reader? Is it missing support for some scripting feature?

Extremely unlikely for v28. We have full support for ES6, ES2016 and ES2017 and growing support for later drafts. More likely is a problem with eBJ's framework or specific use of it.