Follow up to #34141. As pointed out by @maan2003 changing the thinking
parameters invalidates the message cache
([Docs](https://docs.anthropic.com/en/docs/build-with-claude/prompt-caching#what-invalidates-the-cache)).

All the other places where `thinking_allowed ` is set to `false` should
be fine since we do not do any caching there.

Release Notes:

- N/A