docs: updated config docs and tests

ARCHITECTURE.md

@@ -496,7 +496,8 @@ CHATGPT_MCP_REDACT_SECRETS=true
 
 Rules:
 
-- Fail fast if `OPENAI_API_KEY` is missing.
+- Fail fast if `OPENAI_API_KEY` is missing and provider is `openai`.
+- OPENAI_API_KEY is optional for `manual` and `ollama` providers.
 - Do not hardcode secrets.
 - Do not read `.env` content into prompts.
 - Keep context loading disabled by default.
@@ -609,10 +610,10 @@ No external logging service.
 
 ### Configuration errors
 
-Example:
+Example (when using `openai` provider):
 
 ```text
-Configuration error: OPENAI_API_KEY is missing.
+Configuration error: OPENAI_API_KEY is required for the openai provider.
 ```
 
 ### Validation errors