I'm trying to open a document on the ipad. it's a cloud document saved in projects. And I realized that I can't not find any method to access the files saved in projects on ipad.

Hello ​@wise_idealist4482 

Thanks for reaching out. Illustrator on the iPad currently lacks the Projects tab. I understand that this functionality is important to you, and I apologize for its unavailability at this time. Would you mind upvoting the UserVoice for this request (https://illustrator.uservoice.com/forums/931888-illustrator-ipad-feature-requests/suggestions/50860190-add-projects-tab-to-illustrator-home-screen-for) and adding your comments there? Doing this will help us prioritize this request, and you will be notified of any updates.

As a workaround, please try moving the required document to Your Files using the file's menu (3 dots) and let us know if that helps.
 
Feel free to reach out if you have more questions or need assistance. We'd be happy to help.
Anubhav