BrowserRouter history lags behind window.history by one entry

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I have a question about the usage of <BrowserRouter> in an embeddable widget that is used in other applications/pages

I am working on a embeddable App package with internal routing that I will refer to as App A in the following text.
The internal routing is based on the <BrowserRouter> as it is important that a user is able to navigate to a subpath of App A directly using the address bar of the browser. I sadly cannot share its code as its a private repository but a simplified pagestructure looks like this

• / : Landingpage of App A
• /users : List of users of App A
• /settings : Settings of App A

The problem:
App A is embedded in a NextJs environment and displayed under /app (clientside rendering). The app router based routing in NextJs for this is app/app/[[ ... segments]]/page.tsx in order to catch all subpaths of App A on that same page. When navigating directly to a path of App A everything works fine. (Basename of the BrowserRouter is set correctly)

However, there are some navigation elements that should trigger page switches in the UI that surrounds App A on /app. A logo for example, that should redirect to the landinpage of App A. I planned on using the next/navigation hooks to navigate from within the NextJs environment to any App A subpath but I run into some problems.
I would expect the BrowserRouter to react to this, since next/navigation uses the window.history API to manage history state.
And this "kind of works": But it seems like the BrowserRouter is lacking behind the actual history state by one entry.

Example A:

1. I am on the landing page located under /.
2. I use router.push('/app') provided by next/navigation to navigate to App A
3. There is a page change but I get a warning that <Router basename="/app"> can not match URL "/" because it does not start with the basename. Therefore nothing gets rendered

Example B :

1. I am navigating directly to /app unsing the browsers address bar. App A gets rendered correctly
2. I have a button in Nextjs land that should navigate to /users in App A. When clicked the URL changes (/app/users) but the UI does not change.
3. If now I do the same thing with an external button that links to /settings in App A, the URL changes to /app/settings and the BrowserRouter now displays /app/users.

I am currently on v6.25.1 of react-router-dom.

Any idea or input on this?