docs: document codex llm backend

docs-site/content/docs/guides/building-context.mdx

@@ -37,7 +37,13 @@ ktx ingest --all
 ```
 
 Enriched ingest needs a configured model and embeddings. Run `ktx setup` first;
-connections without that configuration fail before any work starts.
+connections without that configuration fail before any work starts. Local-auth
+LLM options include Claude Code and Codex:
+
+```bash
+ktx setup --llm-backend claude-code --no-input
+ktx setup --llm-backend codex --llm-model gpt-5.3-codex --no-input
+```
 
 With `claude-code`, **ktx** agent loops can invoke only the **ktx** MCP tools for the
 current run.

docs-site/content/docs/guides/llm-configuration.mdx

@@ -16,6 +16,7 @@ Set `llm.provider.backend` to one of these values:
 - `gateway`: Use AI Gateway-compatible Anthropic model ids.
 - `claude-code`: Use your local Claude Code session through the Claude Agent
   SDK. **ktx** strips provider-routing environment variables from child processes.
+- `codex`: Use your local Codex authentication through the Codex SDK.
 
 ## Claude Code
 
@@ -47,6 +48,30 @@ model IDs are also accepted.
 metadata may still list host slash commands, skills, and subagents; **ktx** does not
 grant execution access to them.
 
+## Codex backend
+
+Use `codex` when you want **ktx** to run LLM-backed workflows through your
+local Codex authentication instead of a direct provider API key.
+
+```yaml
+llm:
+  provider:
+    backend: codex
+  models:
+    default: gpt-5.3-codex
+```
+
+Configure it non-interactively:
+
+```bash
+ktx setup --llm-backend codex --llm-model gpt-5.3-codex --no-input
+```
+
+This is separate from Codex agent-client setup. `ktx setup --agents --target
+codex` installs instructions and MCP access for an end-user Codex session.
+`ktx setup --llm-backend codex` makes **ktx** itself execute ingest, scan
+enrichment, memory, and other LLM-backed work through Codex.
+
 ## Prompt caching
 
 `llm.promptCaching` has partial parity on `claude-code`. Status and doctor warn