What does this PR do?

resolve_vision_provider_client() in agent/auxiliary_client.py resolves api_mode from config via _resolve_task_provider_model("vision", ...) but never passes it downstream to resolve_provider_client() or _get_cached_client(). This causes vision_analyze and browser_vision to crash when the provider uses a non-default API mode (e.g., api_mode: anthropic_messages for a custom corporate Anthropic proxy).

Additionally, _normalize_aux_provider() had a for_vision branch that incorrectly stripped named custom provider identity (e.g., custom:corp-anthropic → custom) for vision tasks only.

Related Issue

Fixes #8857

Type of Change

• 🐛 Bug fix (non-breaking change that fixes an issue)

Changes Made

Two independent bugs combine:

1. api_mode not propagated: The variable resolved_api_mode is computed at line 1696 but never passed to any of the three downstream call sites. Compare with the non-vision path in call_llm() which correctly passes api_mode=resolved_api_mode. Fixed by adding api_mode=resolved_api_mode to all three downstream calls.

2. Named custom provider lost for vision: _normalize_aux_provider(for_vision=True) returned "custom" instead of the named suffix, losing provider identity needed for config lookup. Fixed by removing the for_vision special case — named custom providers are now preserved for all tasks.

3. Dead code cleanup: Removed the now-unused for_vision parameter from _normalize_aux_provider().

4. Tests: Added 2 targeted tests — named custom provider preservation + api_mode forwarding verification.

How to Test

1. Configure a custom provider with api_mode: anthropic_messages:

   model:
     default: claude-opus-4-6
     provider: custom:corp-anthropic
   custom_providers:
     - name: corp-anthropic
       base_url: https://my-proxy.example.com/anthropic
       api_mode: anthropic_messages

2. Send an image to the agent — vision_analyze should work without crashing
3. Run the test suite: pytest tests/agent/test_auxiliary_named_custom_providers.py -v — all 19 tests pass
4. Run full suite: pytest tests/ -q --ignore=tests/integration --ignore=tests/e2e — passes

Checklist

Code

• I've read the Contributing Guide
• My commit messages follow Conventional Commits (fix(scope):, feat(scope):, etc.)
• I searched for existing PRs to make sure this isn't a duplicate
• My PR contains only changes related to this fix/feature (no unrelated commits)
• I've run pytest tests/ -q and all tests pass
• I've added tests for my changes (required for bug fixes, strongly encouraged for features)
• I've tested on my platform: macOS (Darwin 25.4.0, Apple Silicon), Python 3.11

Documentation & Housekeeping

• I've updated relevant documentation (README, docs/, docstrings) — or N/A
• I've updated cli-config.yaml.example if I added/changed config keys — or N/A
• I've updated CONTRIBUTING.md or AGENTS.md if I changed architecture or workflows — or N/A
• I've considered cross-platform impact (Windows, macOS) per the compatibility guide — or N/A
• I've updated tool descriptions/schemas if I changed tool behavior — or N/A