How local processing works, and how to check it yourself
SumoPDF's PDF tools (organize, modify, convert, and compress) run entirely in your browser. Here is how that works, and how you can confirm it yourself.
The short version
When you choose a file, your browser reads it into memory with the standard File API and hands the bytes to a JavaScript PDF library (pdf-lib) that runs on your device. The tool builds the result in memory and hands it back to you as a download. No step in that chain sends the document to SumoPDF or anyone else.
The path your file takes
Your file goes: browser File API (on your device), then pdf-lib in the page (on your device), then a result held in memory, then a download to your device. No server receives the document, and no upload request is made for these tools.
How to verify it yourself
Open your browser's developer tools, go to the Network tab, and run a tool. You will see the page and its assets load, but no request that uploads your document. You can also disconnect from the internet after the page loads and the browser-local tools still work. The OCR tool additionally downloads its recognition engine and language data once (a few megabytes), then also runs entirely on your device; because OCR uses WebAssembly, the OCR page alone permits WebAssembly in its security policy, but it still uploads nothing.
What still uses the network
Loading the page and its assets (HTML, CSS, the PDF library, images) are ordinary web requests, like any website. Those are separate from document processing, which stays on your device for the browser-local tools.