That you for the clarification. That makes your question in the first post make more sense of what you are seeing.
As to why it is doing that, I don’t have any idea. The plugin is not setup to work that way and it shows a blank form when you are adding a new address. You can see our demo site by registering for an account at https://woo-address-book.crosspeak.dev/my-account/ and you can see how it is working for us.
My best guess would be some sort of conflict with another plugin that you have or your theme that is changing the functionality of the pages so it is loading differently.
If you are able to troubleshoot it on a staging site by disabling plugins and changing to a default theme like Storefront to find out what plugin or theme is causing the conflict that would be useful in allowing us to reproduce the issue to attempt a fix.