You don't see real reasoning tokens with the Chat Completions API; and 'store: false' with Responses really isn't that different to Completions.
FWIW, if you have some tokens to spend, you might want to test Responses vs Completions in intelligence. Since GPT-5 models, we've consistently seen small, but statistically significant and reproducible improvements in intelligence with Responses API vs Completions.
> You don't see real reasoning tokens with the Chat Completions API
That's because there are no "reasoning" tokens. That is the entire point of doing it this way.
One major advantage is that I can switch to a different provider if OAI starts to get weird about this stuff and be able to have a fighting chance of re-adapting my harness to the new vendor's model. If 100% of my reasoning process is outsourced into the proprietary blackbox, there is little hope by comparison.
FWIW, if you have some tokens to spend, you might want to test Responses vs Completions in intelligence. Since GPT-5 models, we've consistently seen small, but statistically significant and reproducible improvements in intelligence with Responses API vs Completions.
However it works underneath the hood, it's real.