Separate page loading from file handling
Every website must load something: HTML, JavaScript, CSS, images, fonts, ads, or badges. Those requests are different from a request that carries your selected file away after you choose it.
The useful question is narrower: did selecting and processing the file add a data-capable request that could contain the file?
Use the Network panel
Open developer tools, switch to the Network panel, and clear the request list immediately before processing. Run the tool, then inspect what appeared afterward.
Look especially for fetch, XMLHttpRequest, sendBeacon, form posts, or upload-like requests. A local result commonly appears as a blob URL created inside the current tab.
Understand the limit of the test
This is an observable browser check, not a formal security audit. It can show whether the processing action created visible upload-style traffic through common browser request paths.
That is still a strong practical signal. A tool that claims local processing should be willing to explain what it measures, what it does not measure, and which third-party hosts the page itself loads.