There are no SDK changes in iOS 13.1 betas (that's why they have letter "A" in the build number instead of "B"). Therefore, they are developing their apps against the latest SDK which is iOS 13.1.
This is why I do think iOS 13.1 will be the final release. Because of the tariffs, Apple packaged many 2019 iPhones with an early release iOS 13 (probably beta 8?). This means that the development of the software installed on 2019 iPhones was ended 1-2 week earlier than previous major releases, iOS 11, for example. There must be a Day 1 patch to these devices when they are released. The launch date will also be the date iOS 13 released to older devices. At this point, I would assume iOS 13.0.1 would be the final release. However, iOS 13.1 is just a bug fix update with enabled features that are disabled in iOS 13.0.
On September 16/17, Apple will release iOS 13. The update will be labeled as "iOS 13" on older devices but it will be shown as iOS 13.1 in About after installing the update (just like iOS 10.0.1 release which was labeled as jus "iOS 10" on older devices but labeled as "iOS 10.0.1" on iPhone 7 devices). The 2019 iPhones will get the same version but correctly labeled as "iOS 13.1" for those devices.
By saying "labeled", I mean the update name shown in Settings->General->Software Update when a new update released. You can see that by checking update on a device that supports iOS 12 but currently running iOS 11. When you check updates on that device, it will just say "iOS 12". But if you install this update it will install iOS 12.4.1 the latest version.