Alexa devices takes 80-100s to start

### The problem

I know this is not necessarily the integrations fault, but with a handful of Alexa devices at home, my HA start is usually blocked for almost 2 minutes because alexa_devices needs that long to start. This blocks the start of zigbee2mqtt and my HA is basically useless before.

The only workaround is to use an automation to disable alexa_devices before reboot and re-enable it after a boot (+ some delay).

### What version of Home Assistant Core has the issue?

2026.9.1

### What was the last working version of Home Assistant Core?

_No response_

### What type of installation are you running?

Home Assistant OS

### Integration causing the issue

Alexa devices

### Link to integration documentation on our website

_No response_

### Diagnostics information

Logger: homeassistant.bootstrap
Source: bootstrap.py:1054
First occurred: 18:19:53 (1 occurrence)
Last logged: 18:19:53

Waiting for integrations to complete setup: {('alexa_devices', '01K7W6T242N4GVBCJ37HC8RZVA'): 1991173.819747481}

Logger: aioamazondevices
Source: components/alexa_devices/coordinator.py:192
First occurred: 18:19:15 (12 occurrences)
Last logged: 18:20:41

Failed to refresh communications settings for device Maximilian's Fire TV, used cached values.
Failed to refresh communications settings for device MaeBKK, used cached values.
Failed to refresh communications settings for device Maximilian's 2nd Fire, used cached values.
Failed to refresh communications settings for device SmartofficeMain, used cached values.
Failed to refresh communications settings for device FireTV2025, used cached values.

### Example YAML snippet

```yaml

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### Anything in the logs that might be useful for us?

```txt

```

### Additional information

Three ideas come to my mind:
- either fix the cause for the issue
- make this a non-blocking task, tell HA you have been started and just load the devices one by one afterwards
- add a new feature in HA to change the integration order or define integrations as non-blocking for startup