tl;dr - yEd Live is hosted in Germany and is generally safe to use with sensitive data.
yEd Live runs locally in your browser and the data never leaves your system. The "Continue last session" functionality only works within your browser by periodically saving the diagram to your browser's local storage.
The ChatGPT feature also only ever sends your direct input to OpenAI in order to create a response from it.
Other than that, yEd Live sends anonymized usage statistics and error reports to our servers to improve the application.
The only functionality that may include any personal data is sending an error report or using the feedback form. You can – but are not needed to - enter your email address in such a report or feedback in order for our support team to get back to you for assistance and bug fixing. So to sum up, unless you explicitly enter your email address and/or name in an error report, yEd Live will not send any personal data to us.
You can also find all of the above information within yEd Live in the "About" panel of the main menu.