I was actually not able to reproduce the problem. I set a different baseURL in the nuxt config and all redirections from the composable and from the server continued to work based on how nuxt handles the redirections internally.
Can you provide a reproduction where this problem occurs?

Hello,
unfortunately, I have the same issue with baseURL. The problem is that there are two applications: one is hosted on NUXT_PUBLIC_SITE_URL (mysite.com) and the other one on NUXT_PUBLIC_SITE_URL/BASE_URL (mysite.com/v2)

The redirection from the composable is not possible, the provider simply calls mysite.com/auth/login which is completely different web app. I could make it through the ugly hack, instead of login() used /v2/auth/login.

However, I have another issue with callbackRedirectUrl.

nuxt.config.ts
//...
 providers: {
      keycloak: {
         //...
         callbackRedirectUrl: '/v2/home'
        //..
}

The callback redirection is working fine on dev mode, but on prod mode the calback redirect url is always /. For publishing IIS setup is used.
I hope that at least the first issue could be solved by proposed changes in the PR, however not quite sure about the last one with callbackRedirectUrl.