Problem
With the change to just use the url.host, calls to different models by the same provider are not separately cached.
Solution
Update the _key method so that it uses the url.copy_remove_param('key') when creating the cache key. This caches the full url with the model name (e.g. https://generativelanguage.googleapis.com/v1beta/models/gemini-2.5-flash:generateContent) allowing for unique cache by model.