Display reasoning summary, and check readiness for reasonning

[FelixMalfait]

• Go through https://platform.openai.com/docs/guides/reasoning and https://platform.openai.com/docs/guides/reasoning-best-practices
  , make sure we are doing everything according to best-practises (e.g. the way previous response is passed, that reasoning tokens are taken into account in billing, etc.). Maybe there is nothing to do.
• Display reasoning summary. We want to be able to see how the model think (similar to how Cursor does it where it's shown during thinking, and then hidden but you can click on "thought for x" to view the reasoning summary)