How can the manager add additional products or notes to the reservation for internal purposes? They should not be visible to customers.

Select the required field type and create it. You can find a detailed guide on creating and configuring fields here.

After creating the field, open its settings and enable the Show only to managers checkbox.

This field will not be displayed on the booking form for the client. It will also not be shown to the client in message templates by default.

If you want the field to be displayed in the message to the client, you need to make changes to the corresponding message template. For instructions on working with templates, see here.