Three ways a browser can speak
A website can call the browser's built-in SpeechSynthesis API, run a downloaded neural model, or send text to a speech service. The page appearing in a browser does not tell you which path it uses.
TTS Lines' free local voices download their models from a public host and generate audio in the browser. The script and generated audio stay on your device during that free workflow. Loading the site and model still makes network requests.
The tradeoff
Local generation avoids sending the script to a speech API, but the model can be large and needs device memory. It may take a while to load the first time or on a device that has cleared its cache.
Cloud services can offer more voices and process work away from the device. They require sending the relevant text to the service. Read each product's privacy terms and the label on the selected voice rather than treating all browser tools as local.
A practical check
Before a long script, generate one harmless line. Note whether the interface labels the voice as local or cloud, whether an account is required, and whether the tool can export the file you need. Keep your own copy of the original text; browser storage is not a backup.