There aren't really any steps to reproduce, other than to say that Orion's tabs are invisible to the Accessibility API. This causes two issues. The most important issue is that users with disabilities will be unable to navigate Orion's tabs using macOS' built-in accessibility features. Safari, Chrome, and Edge all have tabs that are fully functional with the Accessibility system, which is where these users will head.
The second issue is that there are a number of apps that work with other apps' windows and tabs, and these apps will be unable to support Orion. One such example is our own Witch, which allows users to switch directly to windows in any application, and directly to tabs in applications that have macOS Accessibility support in their tabs.
Witch cannot see Orion's tabs—either vertical or horizontal. That's because those tabs don't exist in the Accessibility system. The "easy" way to solve this is to use Apple's standard tab APIs (as that would automatically include Accessibility support), but I expect you have many good reasons for doing what you did. Another solution would be to look at TextEdit's tabs using Accessibility Inspector, and then make your tabs convey those same details to the Accessibility API. This wouldn't involve changing how your tabs are designed, but just having them generate some additional information for the Accessibility API to use.
The advantage for us, of course, is that Witch will now be able to see and switch between Orion's tabs. But the bigger-picture advantage for Orion is that your app will be more usable by individuals who rely on the Accessibility features in macOS to use their Macs. They are always grateful for apps that have full Accessibility API support.
If you don't have any experience with Accessibility API programming on macOS, here are the references we rely on for help:
Thank you for considering these changes that will not only help our mutual users, but anyone who relies on the macOS Accessibility system's features.