Browsers offer an "anonymous" or "private" or "incognito" mode. Does this mean that no one can see what you do on the internet?
No! This only means that the browser does not save what you have done on the internet. Nothing else changes - the Internet/WLAN router and also the Internet provider continue to record which websites you visit.
True anonymity on the Internet is therefore extremely difficult to achieve. However, in order to surf without saving advertising cookies or so that other users of the computer do not immediately see what you have done on the Internet, the "private" mode is just the right thing.