Feature: Better Support for Aggressive Corporate Proxy Timeouts

### Checks

- [x] I have searched [github.com/aws/amazon-q-developer-cli/issues](https://github.com/aws/amazon-q-developer-cli/issues?q=) and there are no duplicates of my issue
- [x] I have run `q doctor` in the affected terminal session
- [x] I have run `q restart` and replicated the issue again

### Operating system

Mac

### Expected behaviour

Proxies such as bluecoat have pretty aggressive timeouts, e.g. 10/15s. This does not play well with what appears to be the keepalive configuration within Q Developer. Perhaps this could be configurable to lower the timeouts to align with upstream proxies and/or disable keepalives?

### Actual behaviour

Q often hangs during longer requests than 15s and eventually times out after a while:

```
Amazon Q is having trouble responding right now:
0: dispatch failure (timeout): request timed out: error sending request
1: dispatch failure
2: timeout
3: request timed out: error sending request

Location:
crates/chat-cli/src/cli/chat/mod.rs:819

Backtrace omitted. Run with RUST_BACKTRACE=1 environment variable to display it.
Run with RUST_BACKTRACE=full to include source snippets.
```