docs(providers): say how a custom provider uses the Responses wire

#6997 asks for custom providers to be able to use `/responses`. They
already can. A `[providers.<name>]` table with `wire = "responses"`
resolves to WireFormat::Responses (client.rs
provider_wire_format_for_config, the ProviderKind::Custom branch). The
existing subagent route-replacement test proves such a table posts to
`<base_url>/responses`. Neither CONFIGURATION.md nor PROVIDERS.md said
so: both described custom tables as OpenAI-compatible Chat endpoints
only. Both now say that Chat Completions is the default and that `wire`
selects Responses or Anthropic Messages, and CONFIGURATION.md gives a
custom-table example.

Verification: docs only. Checked the keys against the code: `kind`,
`base_url`, `api_key_env`, `model` and `wire` are all read for custom
tables (provider_readiness.rs, model_inventory.rs, config.rs
provider_wire_dialect). `git diff --check` is clean. No live gateway was
called.

Refs #6997

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NBKbhx19BRbZtvWK8rVKjz

docs/CONFIGURATION.md

@@ -601,6 +601,19 @@ Custom provider names may be selected with `provider = "<name>"`,
 `--provider <name>`, or an AgentProfile `provider = "<name>"` when the matching
 `[providers.<name>]` table exists.
 
+A custom table sends Chat Completions requests by default. Add
+`wire = "responses"` to send OpenAI Responses requests to
+`<base_url>/responses` instead, or `wire = "anthropic"` for Anthropic Messages:
+
+```toml
+[providers.my-gateway]
+kind = "openai-compatible"
+base_url = "https://gateway.example/v1"
+api_key_env = "MY_GATEWAY_API_KEY"
+model = "gpt-5.6"
+wire = "responses"
+```
+
 StepFun has a first-class provider entry, so keep Coding Plan credentials and
 base URL scoped to `[providers.stepfun]`:
 

docs/PROVIDERS.md

@@ -384,7 +384,9 @@ Instead, choose the closest shipped route and override its endpoint/model:
 - Multiple named OpenAI-compatible gateways, or local routes you want to pin
   from an AgentProfile, can use a custom table such as
   `[providers.lm-studio] kind = "openai-compatible"` and select it with
-  `provider = "lm-studio"` or a profile `provider = "lm-studio"`.
+  `provider = "lm-studio"` or a profile `provider = "lm-studio"`. Such a table
+  speaks Chat Completions unless it sets `wire = "responses"` (OpenAI
+  Responses at `<base_url>/responses`) or `wire = "anthropic"`.
 - Local OpenAI-compatible runtimes: use `provider = "vllm"`, `"sglang"`, or
   `"ollama"` with the matching provider-specific base URL/model values.