The default context is set to 'Last 10 pairs'; project settings have no context property. New chats are created with 'No Context' (visible in chat settings).
This means that if I want to use projects, I have to edit the context setting for every new chat.
Solution:
Add context to project settings
Ensure defaults carry over unless modified
Global settings:

Project model settings:

Project chat settings:

Please authenticate to join the conversation.
Completed
Feature Requests
10 months ago

Andrey
Get notified by email when there are changes.
Completed
Feature Requests
10 months ago

Andrey
Get notified by email when there are changes.