Thanks for the support.
I’ve found the answer already. From my testing and observations, web search was being triggered on every model I used (or at least every model I tried), even after switching models. This appears to be an issue on the provider side.
The problem is that web search becomes an unwanted, hidden cost that I can’t properly control or fully disable, even when it’s not needed.
I’ve already cleared my account, cancelled the service with this provider, and I’m now looking for a different provider.
Thanks again.