Custom model providers (COPILOT_PROVIDERS_CONFIG / COPILOT_PROVIDER_*) are ignored in --host-environment and --server modes #5371

Describe the bug

Custom BYOK model providers configured via COPILOT_PROVIDERS_CONFIG (providers.json) or COPILOT_PROVIDER_* environment variables work in interactive TUI and -p prompt modes, but are ignored when running copilot --experimental --host-environment <name> or copilot --server. Remote sessions created from GitHub Mobile/Web only expose and use built-in GitHub Copilot models instead of the configured custom provider.

Affected version

@github/copilot 1.0.106-9 (Linux ARM64 / x64)

Steps to reproduce the behavior

1. Configure a custom OpenAI-compatible provider in /tmp/providers.json:

   {
     "providers": [{ "name": "gateway", "type": "openai", "baseUrl": "https://gateway.example.com/v1", "wireApi": "responses", "apiKey": "..." }],
     "models": [{ "id": "my-model", "provider": "gateway", "modelId": "my-model" }]
   }

2. Verify it works in prompt/interactive mode:

   COPILOT_PROVIDERS_CONFIG=/tmp/providers.json copilot --experimental --model gateway/my-model -p "1+1"

   (Succeeds and routes to https://gateway.example.com/v1 with isByok: true in ~/.copilot/session-state/<id>/events.jsonl.)
3. Start a remote environment host with the exact same configuration:

   COPILOT_PROVIDERS_CONFIG=/tmp/providers.json COPILOT_MODEL=gateway/my-model copilot --experimental --host-environment my-host

4. Create a session on my-host from GitHub Mobile/Web and send a prompt.
5. Check ~/.copilot/session-state/<id>/events.jsonl: gateway/my-model is never listed in the model picker, and turns execute against "providerId": "copilot" instead of the custom provider.

Expected behavior

--host-environment and --server modes should load COPILOT_PROVIDERS_CONFIG / COPILOT_PROVIDER_* into created sessions so custom provider models appear in the remote session model picker and are used for inference.

Additional context

Setting COPILOT_PROVIDER_BASE_URL, COPILOT_PROVIDER_API_KEY, and COPILOT_MODEL via environment variables exhibits the same behavior: respected in interactive/-p mode, ignored in --host-environment and --server modes.