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processing.algorithmHelp('qgis:zonalstatistics') prints out:

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Outputs
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INPUT_VECTOR:  <QgsProcessingOutputVectorLayer>
        Zonal statistics

but I'd like to redirect the output to a CSV file with only the id column of the INPUT_VECTOR and the output of the Zonal statistics algorithm. Is this possible??

Is there some way to redirect the output?

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Unless you modify the source code for the script, it will just save the attributes to the input vector file. A possible alternative could be to run the algorithm and then export the input layer as a csv file with only the fields you're interested in:

layer = iface.activeLayer()
output_path = 'path/to/output.csv'
zone_stats = ("id", "Count", "Sum", "Mean")
field_list = [layer.fields().indexFromName(fields.name()) for fields in layer.fields() if any(s in fields.name() for s in tuple(zone_stats))]
QgsVectorFileWriter.writeAsVectorFormat(layer, output_path, "UTF-8", driverName="CSV", attributes=field_list)
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