Locale change issue with basePath and localePrefix = 'as-needed'

[SpasiboKojima]

Description

Locale simply doesn't change, seems to be related with the incorrectly applied cookies.
Unfortunately I can't reproduce it in codesandbox, only when running localy. Tried in Chrome and Firefox, shouldn't be exclusive to my setup.
Another way to reproduce it to basically add basePath: '/s', to next.config.js and localePrefix = 'as-needed' to src/config.ts in your examples/example-app-router/.

locale.mp4

Verifications

• I've verified that the problem I'm experiencing isn't covered in the docs.
• I've searched for similar, existing issues on GitHub and Stack Overflow.
• I've compared my app to a working example to look for differences.

Mandatory reproduction URL

https://codesandbox.io/p/github/SpasiboKojima/next-intl-bug-repro-app-router/main

Reproduction description

Steps to reproduce:

1. Open reproduction
2. Change locale to German, see it set another cookie on / path
3. Try to change locale back to English

Expected behaviour

Expected it to change locale and probably to not set another cookie

[amannn]

Many thanks for the great bug report! This will be fixed in #999.

[SpasiboKojima]

Many thanks for the great bug report! This will be fixed in #999.

Great job, thank you very much!