Hi Segolene Menin,
Thank you for posting back and confirming the scenario with us.
We have finished tests in Project for the web app and To Do app.
As Dale Howard pointed out, the tasks created in Project for the web app and assigned to you or other team members won't appear in the To Do app, because they are 2 separate applications and don't integrate with each other.
Very sorry for the inconvenience caused. We do understand it affects your work and apologize for it.
Given this situation, we sincerely recommend sharing your valuable feedback to Project feedback community and Microsoft To Do community.
Other users also noticed this limitation. You may also vote for these similar ideas:
Integrate with “Project for the web”
My assigned tasks from “Project for the web” to show up in “Assigned to me” like we can with “Planner”.
This is the best way to let the developers know which features are important to you, know your requirements and comments, help to improve the product and make it better for you and others.
Your understanding is highly appreciated.
Hope you have a safe and happy new year!
Best regards,
Tina