You need one more basic text column in your chat table. You can’t assign a session or page ID if you haven’t providing a column in your table to write that ID into.
Add a column in your chat table to hold a value such as your page ID. When you do that, then it will show up in your ‘Save Data’ configuration in the chat component configuration. You need to give it a column to store a value. Then you can fill it and use it for filtering.