Everything happens in your browser
When you open a file, your browser reads it from your disk into the page's memory. The tool works on it there and hands you the result as a download. At no point is the file sent anywhere: the site has no upload endpoint.
On-device speech recognition
Audio to text uses Whisper base, an open speech recognition model released by OpenAI under the MIT license. The first time you use it, your browser downloads the model, about 80 MB, from audio.scissor.studio and keeps it in its cache. The model then runs in a background worker with WebAssembly, on your processor. Your browser decodes the audio, converts it to the 16 kHz mono sound Whisper expects, and the worker turns it into text in 30-second windows.
MP3 tags
Song titles, artists, album art and lyrics are stored in an ID3 tag at the start of an MP3 file. The MP3 tag editor reads that tag, lets you change it, and writes a new file with the new tag in front of the untouched audio, so the sound is copied bit for bit.
Check it yourself
Open your browser's developer tools, choose the Network tab and use any tool. You will see the page and the model load from audio.scissor.studio, and nothing go out when you open a file. You can also turn off your connection after the page has loaded: every tool keeps working.