1. Activate developer mode
2. Go to Settings > Technical > Database structure > Models
3. Search for model mrp.production and open it
4. Add a new field named x_project_id with parameters shown in the attached screen shot "Selection_034.png"
5. Go to Manufacturing > Operations > Manufacturing Orders and open one
6. From debug menu click to see the dropdown menu then click the menu item "Edit Form View". See attached "Selection_036.png"
7. Edit the architecture as seen in the attached scree shot "Selection_037.png" then save it.
8. Reload the page (Ctrl+F5, or Command+R if you are on Mac) to see the project field is now on the Manufacturing Order form.

Now, you are almost done. Just a few more steps to ensure future updates will not revert your customization:

1. Do the step 6 above
2. Click on the link in the field Model data. See attached "Selection_039.png"
3. Check Non Updatable then save.

Hope this could help!