By default a filter is meant to search for an issue.
What you are asking might be easier to do via the REST APIs.
Have you considered that?
The REST end point is:
More info can be found here: https://docs.atlassian.com/jira/REST/latest/#d2e2046
A filter has nothing to do with the data displayed, it returns a list of issues.
If you want to get data from a filter, you need to put the filter through a report of some sort, such as the issue navigator.
By dfinition, the issue navigator shows you issues. If you want project data in it, include the field "project" and you'll see what each issue belongs to.
If you want just project names, then you need a report that will read the list of issues and extract that.
I'd suggest a simple one - create a dashboard for yourself, and add a "filter statistics" gadget. Select your filter as the data source, and then select "project" as the field to group the results by. You'll get one line per project in your filter, with a count of matching issues next to it.
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