Not redirected after entering a password on the admin panel when using OIDC SSO

### Environment

self-hosted (https://develop.sentry.dev/self-hosted/)

### Steps to Reproduce

I'm creating an issue on behalf of a customer.

> Hi! I am having trouble accessing the admin panel in Sentry. I use OIDC SSO (https://github.com/siemens/sentry-auth-oidc) to log in. The account is a superuser and has a password.
>
> I can't find a button anywhere in the Web UI to go to the admin panel. When I go directly to https://sentry.example.com/manage/, I am asked for a password, which I successfully enter, but nothing happens (the browser's network requests show that the request to /api/0/auth/ is successful)

from @saph1s on Discord (https://discord.com/channels/621778831602221064/1436336001529286666)

> [@aldy505](https://github.com/aldy505) This is a known issue also for us since the beginning of the plugin. We don't really know why this happens, but if you click on `sign-out` and sign back it, it should show up.

from @max-wittig (https://github.com/getsentry/self-hosted/issues/4022#issuecomment-3503145630)

### Expected Result

When user successfully entered their password as a authorization confirmation, they should be able to see admin-related content.

For sentry employees: Saph1s sent me a video to reproduce the behavior. Let me know on Slack if you want the link.

### Actual Result

HTTP request to `/api/0/auth` is successful, yet users don't get redirected.

### Product Area

Settings

### Link

_No response_

### DSN

_No response_

### Version

25.10.0

Reproduce the issue on a self-hosted Sentry 25.10.0 instance using OIDC SSO, then inspect the successful request to /api/0/auth/ and the subsequent navigation to /manage/. Done means that entering the password redirects the superuser to the admin panel and displays admin-related content without requiring sign-out and sign-in.

Written by the indexing model from the issue text.