Most frontier Models won't show you their true reasoning, but only a summary.
There is also no reason you can automatically assume the quality and price of the outcome based on the first few reasoning trace summaries.
If you look at the recent model releases, it becomes clear that the trend is that the largest models provide the most cost-effective solutions, because of the massive turn/tool call/reasoning reduction needed to find the solution, compared to cheaper and smaller models.
The largest models are very well known for having large reasoning traces. The thing that cracks down on overthinking is reasoning-effort training, which is largely a function of how the model is trained (certain RL objectives/teachers) rather than size of the model. The Kimi K3 technical report has some excellent work on this: https://arxiv.org/pdf/2607.