Yes, if the chat is activated, you can save the chat after the first message has been transmitted. To do this, open the chat window and use the button with the three dots to open the chat menu. Then, select the "Save Chat" option.
In the settings at https://tuwien.zoom.us/profile/setting, you can restrict the saving of the chat by participants. However, this does not prevent them to take screenshots or manual transcription by hand.
Keyboard Shortcuts: Show/Hide Chat Panel
- Windows: Alt+H
- MacOS X: Command(⌘)+Shift+H
- iOS: Command + Shift + H