Unplug your network cable when you use it.

And it stores it in local storage and uploads it using a service worker later when I'm online?

If that's your paranoia level: How do you know the "offline" tool you're using is not uploading to a server? Possibly inadvertently in the course of bug reports, or surreptitiously while contacting the license server...?

Should security concerns really warrant not trusting the (reputable) vendor that the files are not being uploaded, you would need to do some sort of audit and/or run in an isolated environment and wouldn't be the "random user" referred to in OP.

You can easily block network access for an app on Windows using Windows Firewall. Same on a few Android skins such as MIUI by Xiaomi

same is true for Chrome Browser, open dev tools and select Network to "Offline"

Thanks

Use incognito mode then close that window before reconnecting online?

I'd suggest install a separate browser (there exists a myriad by now), unplug internet, use the service, uninstall the separate browser, reboot pc.

I suggest a separate VM for that, that you can delete when you're done. Add put the VM on a separate PC that you bought with cash off craigslist. Then toss the PC away in a different postcode when you're done. Then you can use the PDF tool safely without fear you're being tracked.

Run it on an air gapped breadboard 8086?

Use 'Developer Tools' and Inspect. Watch the Network tab.

If you also wear a tinfoil hat, delete the local storage, etc, after you are done using it.