Assist timeout in Carplay isn't configurable

**iOS device model, version and app version**

Model Name: iphone
Software Version:
App version: stable

**Home Assistant Core Version**

**Describe the bug**
I'm using a local LLM that takes longer tham 60s to respond. The carplay UI shows an Error prematurely. Sometimes, it will then eventually transition from Error to Responding

**To Reproduce**
Give an Assist prompt to a local LLM via Carplay interface
The prompt takes about 90s to generate a response
Error is shown on Carplay screen in the middle of Processing
**Expected behavior**

**Screenshots**

**Additional context**

Start at the CarPlay interface's Assist prompt flow and locate where the 60-second processing timeout is applied. Verify the behavior with a local LLM that takes about 90 seconds, then confirm the timeout can be configured and that the CarPlay UI does not show an error before the configured limit.

Written by the indexing model from the issue text.