What does this PR do?

When auxiliary models (vision, web_extract) use _read_main_provider(), they get the literal string "custom" for model.provider if the user configured a custom endpoint. But _get_named_custom_provider() and _resolve_vision_provider() expect a provider key name that exists in the providers: dict — they look up credentials, defaults, and client adapters by that key. This mismatch caused auxiliary tasks to fail with None provider resolution.

The fix enhances _read_main_provider() in agent/auxiliary_client.py: when the bare "custom" provider is detected, it searches the providers: dictionary for an entry whose api, url, or base_url matches the model base_url. If found, it returns the actual key name instead of "custom". This bridges the gap between config-time naming (what users put in providers: my-local) and runtime lookup (what auxiliary resolution code expects).

Related Issue

Fixes #14676

Type of Change

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

Changes Made

• agent/auxiliary_client.py: Added base_url matching logic in _read_main_provider() that iterates providers: entries and returns the first key whose api/url/base_url matches the model configured base_url (with trailing-slash normalization). Falls through to bare "custom" if no match.
• tests/agent/test_auxiliary_named_custom_providers.py: Added 6 test cases covering: bare custom with matching providers entry, bare custom with no match, providers entries using "base_url" key, non-custom passthrough, absent providers dict fallback, and trailing slash normalization.

How to Test

1. Run the new tests: pytest tests/agent/test_auxiliary_named_custom_providers.py -o addopts= -v
2. Run the full auxiliary test suite: pytest tests/agent/test_auxiliary*.py -o addopts= -q (all 142 pass)
3. For an integration test, configure a named custom provider in config.yaml and verify auxiliary tasks (vision model, web extract) resolve it correctly via the _read_main_provider() mapping.

Checklist

Code

• Read Contributing Guide
• Commit messages follow Conventional Commits (fix(scope):)
• Searched for existing PRs — this is not a duplicate
• PR contains only changes related to this fix (no unrelated commits)
• All tests pass: pytest tests/ -q
• Added tests for my changes
• Tested on: Ubuntu 24.04

Documentation & Housekeeping

• N/A — docstring updated in _read_main_provider()
• N/A — no config key changes
• N/A — no architecture or workflow changes
• N/A — no cross-platform concerns
• N/A — no tool schema changes

Screenshots / Logs

Test output:

tests/agent/test_auxiliary_named_custom_providers.py ... 25 passed in X.XXs
All 142 auxiliary tests pass.