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You set feature fields to empty QgsFields.

fields = QgsFields() # fields is empty
feature.setFields(fields) # you set the empty fields

Instead, pass layer.fields() to QgsFeature.

feature = QgsFeature(layer.fields())

You also get NULL values, because you add the feature to the layer (provider.addFeatures([feature])) before you populate the fields.

Use this script:

srcFile = "D:\\Data\\filename.csv"

layer = QgsVectorLayer("Polygon?crs=EPSG:2193", "Polygons", "memory")
QgsProject.instance().addMapLayer(layer)

provider = layer.dataProvider()
provider.addAttributes([QgsField('ViewName',QVariant.String, '', 50, 0),
                        QgsField('FigName',QVariant.String, '', 10, 0)])
layer.updateFields()

with open(srcFile,'r') as infile:
    rows = infile.readlines()

for r in rows:
    parts = r.split(',')

    xMin = float(parts[2])
    yMin = float(parts[3])
    xMax = float(parts[4])
    yMax = float(parts[5])

    rect = QgsRectangle(xMin, yMin, xMax, yMax)
    polygon = QgsGeometry.fromRect(rect)
    
    feature = QgsFeature(layer.fields())
    feature.setGeometry(polygon)
    feature['ViewName'] = parts[0]
    feature['FigName'] = parts[-2]
    provider.addFeatures([feature]) 

Sample CSV:

1,0, 1804512.8556, 5453390.58088, 1813512.8556, 5461390.58088, yedi1, sekiz1, dokuz1
2,0, 1814512.8556, 5473390.58088, 1823512.8556, 5471390.58088, yedi2, sekiz2, dokuz2

Result: