### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

## Summary

> NOTE: This bug report was partially generated using an LLM. However, the results were manually validated and the workaround is currently in use.

Two related bugs cause `ssl_verify: false` to be silently ignored in specific code paths:

1. **`BaseLLMAIOHTTPHandler` never accepts `ssl_verify`** — the constructor has no `ssl_verify` parameter, `_get_or_create_transport()` calls `AsyncHTTPHandler._create_aiohttp_transport()` without SSL args, and `_make_common_async_call()` calls `client_session.post()` without an `ssl=` kwarg. The result: aiohttp applies a default SSL context even on plain `http://` URLs.

1. **`AsyncHTTPHandler` retry path drops `ssl_verify`** — on `ConnectError`/`RemoteProtocolError`, the `post()`, `put()`, `patch()`, and `delete()` methods call `self.create_client(timeout=..., event_hooks=...)` *without* forwarding `ssl_verify`. The default (`None`) resolves to `True` via `get_ssl_configuration()`, so the retry attempt has SSL verification enabled regardless of the original setting.

## Affected code paths

| Pat…