Fixes#67278. Since config v12 (see #8776), custom_providers: list is
legacy — the migration converts it to the providers: dict and the
resolver reads the dict first (runtime_provider.py). Docs still taught
the legacy list as primary.
- integrations/providers.md: all 8 YAML examples converted to
providers: dict (field mapping code-verified: api, default_model,
transport), one consolidated legacy-format note
- configuring-models.md, configuration.md, credential-pools.md,
migrate-from-openclaw.md, provider-runtime.md, faq.md: examples and
prose flipped to dict-first; legacy list noted as still-read
- adding-providers.md untouched (sole mention is a literal test
filename)