Tasks start out private to whoever created them. A private task can still use a project's brief, files and intelligence as context, so you can work with everything the team knows without your chat showing up in the project.
Private vs. shared
Private task - only you can open it. Above the prompt box it says Only you see these messages. Tasks you start from the home page are private.
Shared task - it lives in a project, and everyone with access to the project can open it. Above the prompt box it says Everyone with project access sees these messages.
Use a project as context in a private task
In the prompt box, click the Multiply logo next to the attachment button.
Under Choose context, search for a project and select it. The project now shows as a chip in the prompt box, and the task reads "This task uses context from project project."
To share the task with the project later, click the Share icon in the top right of the task.
To stop using the project, click the × on the chip. The task stays private either way.
Move a task into a project
Open the task and click the Share icon in the top right.
Under Destination, pick a project. Pick Private to make a shared task private again.
Leave All files will move with the task ticked to bring the task's files along.
Click Move.
Only the person who created a task can move it. Archived tasks need to be unarchived first. The task gets a new link after a move, so share the new one.
Opening someone else's private task
If a colleague sends you a link to their private task, you'll see This task is private and the name of its owner. Ask them to move it into a project you both have access to and send you the new link.