bug: coder_signed_app_token is not renewed when an Authorization header is sent

### Is there an existing issue for this?

- [x] I have searched the existing issues

### Current Behavior

I am using Coder to develop a web application with both frontend and backend components running in the same workspace pod, on kubernetes. The web application serves pages on port `8080`, while the backend listens on port `8081`.

To preview my application, I share both ports, which are accessible via the subdomain: `https://port--agent--workspace--username.coder.example.com`. Backend requests (port `8081`) requires an Authorization header, and because of that, they never reach the workspace.

Coder verifies that the user is authorized to access the subdomain using the `coder_subdomain_app_session_token_*` session cookie and the `coder_signed_app_token` short-lived cookie.

When the `coder_signed_app_token` expires, the `coder_subdomain_app_session_token_*` is used to renew it. However, if any Authorization header is sent, the `coder_subdomain_app_session_token_*` is ignored: you get a redirect to the `/applications/auth-redirect endpoint` (which for a backend call requires manual handling in the code to follow and re-authenticate)

### Relevant Log Output

```shell

```

### Expected Behavior

When accessing a Coder app, if the `coder_subdomain_app_session_token_*` cookie indicates that the user is authorized, the request is forwarded to the workspace agent along with the Authorization header. Additionally, a `coder_signed_app_token` cookie is sent back to the caller.

### Steps to Reproduce

1. Start a basic coder workspace
2. Upsert a workspace agent port share from the workspace dashboard (Open Ports > Share Ports > 8080 HTTP Authenticated). It doesn't meter weather a process is listening on that port.
3. Visit `https://8080--agent--workspace--username.coder.example.com`
4. Inspect the browser and copy the `coder_subdomain_app_session_token_*` cookie
5. Send curl requests to reproduce, with and without Authorization header

```
curl -v --cookie "coder_subdomain_app_session_token_*=TOKEN" https://8080--agent--workspace--username.coder.example.com/

< HTTP/2 200
< set-cookie: coder_signed_app_token=TOKEN
(This works as expected. We also get the coder_signed_app_token that will be used until expired)
```

```
curl -v -H "Authorization: bearer whatever" --cookie "coder_subdomain_app_session_token_*=TOKEN" https://8081--agent--workspace--username.coder.example.com/
< HTTP/2 303
< location: https://coder.example.com/api/v2/applications/auth-redirect?redirect_uri=https%3A%2F%2F8081--agent--workspace--username.coder.example.com%2F
(This request doesn't reach the workspace pod. Moreover, no coder_signed_app_token cookie is sent)
```

### Environment

- Host OS: k8s deployment, helm chart version 2.27.8
- Coder version: v2.27.8+42f06c8

### Additional Context

_No response_