How can I make a consistent structure in the database (ER-model)?

Question

Database design

The bottom line is that all tables should be connected sequentially, there should not be circular connections, as it is now in the diagram.
There are tables Users, Projects, Tasks, Messages.
The user can create a project, tasks in the project. When you create a project, a chat belonging to this project is created. All users in the project can write to this chat.
Users can create tasks in a project that have fields:
- project_id (id of the project to which the task belongs)
- creator_id (id of the creator of the task)
- performer_id (id of the performer)

The point is that the user is associated with the project once, and now he is connected three times: via chat, via task and directly

Answer 1

In Taskshould be references not to User, but to Project_User (id). After all, only those who work with the project can create and perform tasks.

a chat belonging to this project is created

Why are you the opposite? Several projects are linked to one chat.
If the chat is limited to project members, then you can delete Chat, and in Messageshould refer to Projectand Project_User (id).
And in Project_Userthere should be a link to a separate table Role (ID, Name). Don't break third normal form.
I propose a universal structure Chat:
ID
Name. "Game" for example.
ProjectProject, "Game, balls", for example. If NULL - common.
RoleRole - group by role, "Game, balls, tester", for example. If NULL - common for the project. If the project is also NULL, it is generic by role. "Game, tester", for example.