Looks like ScriptRunner doesn't fancy some collection functions in JQL.
For example, a query:
project = ABC and "Project Link" is NOT EMPTY
would produce an error "The operator 'is not' is not supported by the 'Project Link' field."
On the other hand this JQL works fine and basically produces the expected results
project = ABC and "Project Link" != ABC-0001
where "Project Link" is my customField of IssuePicker type with single value select
While this particular workaround solves "is not empty" case, the other function i.e. "in (<subset>)" doesn't work.
I suspect that " Issue Picker searcher" component is broken/incomplete. Anybody else ran into the same problem?