your understanding needs to be that you are creating a connection TO the project object in order to run searches on it. As such, a lot of your "project" mentions are not applicable. You also have a bit of the wrong syntax (again, look to what would normally show up in a project report if you have ANY questions at all).
Here's an example or two:
if on your project report, youfilter on the program ID field, and switch to text mode, you'll see the filter is referencing a field called programID. You have this in your exists filter as "project:program:ID" -- please use programID instead.
if on your project report you filter on a particular custom field, and switch to text mode, you might see the filter is referencing a "DE:customfield". So, no need to put the "project" part in, if that's the case.
TLDR: build the filter as you normally would in a project report, then switch to text mode and add exists:a: in front of your filtering lines. Also use the project report to discover what syntax you should be using.
