[Bug]: AMP not working: stuck in login loop

### Describe the bug

Core
2026.7.4
Supervisor
2026.07.5
Operating System
15.2
Frontend
20260624.6

amp 5.15.7

stuck in login loop .

### To Reproduce

try login

### Expected behavior

to login .. but its stuck

### Screenshots

_No response_

### Home Assistant Version

2026.7.4

### Alexa Media Player Version

5.15.7

### Alexa Media Player API library Version

1.29.25

### Have you entered a 52-character key for Amazon 2SV via Authenticator App login?

Yes

### Is the HA core integration Alexa Devices installed?

Yes

### Amazon Domain

amazon.com (US)

### Amazon Domain (if Other)

_No response_

### Debug Logs (alexa_media & alexapy)

```text

```

### Additional context

_No response_