I have found that all filed are joined with an AND so I can't do querys like "It's assigned to me OR it's a project that I own".

It can be done globally, for example an option to join all field with OR instead of AND. Or better if you can use an in query modification, for example in user assigned: "OR PhoneixS" and in projects "OR Maniphest" to specify that it must query all task that are assigned to me or to Maniphest project.