docs: add caveat about ContextVar in dependencies

As discovered and discussed in #13382, ContextVars set in a
_synchronous_ dependency is not available to the rest of the request due
to the way FastAPI handles that dependency.

The documentation did not make any mention of this, and it was only
after I asked that I discovered this was intended behaviour. So I am
updating the docs to make this clear to others.

Ref: #13382
Signed-off-by: JP-Ellis <[email protected]>

docs/en/docs/tutorial/dependencies/index.md

@@ -156,6 +156,12 @@ If you don't know, check the [Async: *"In a hurry?"*](../../async.md#in-a-hurry)
 
 ///
 
+/// warning
+
+If you need to rely on `ContextVar` values across multiple steps in a request, **use an async dependency** or another approach. This is because sync dependencies are executed in the mainthread*, while `async` dependencies run in the same thread pool as the one handling the request. As `ContextVar` provides thread-local storage, any value set inside a sync dependency will not be available in the rest of the request handling.
+
+///
+
 ## Integrated with OpenAPI
 
 All the request declarations, validations and requirements of your dependencies (and sub-dependencies) will be integrated in the same OpenAPI schema.