Summary

• Read model.api_key from gateway config when handling /model commands.
• Pass the configured key into the existing model switch path so authenticated custom endpoints can be probed.
• Add a gateway regression test that asserts /model uses the configured API key.

Fixes #18681

Tests

• scripts/run_tests.sh tests/gateway/test_model_command_custom_providers.py
• git diff --check origin/main...HEAD