Found you can addApply the symbologyExport=QgsVectorFileWriter.FeatureSymbologysymbologyExport=QgsVectorFileWriter.FeatureSymbology parameter when writing and it will keep its symbology when opened in MapInfo.
QgsVectorFileWriter.writeAsVectorFormat(vlayer, path_to_tab, 'utf-8', driverName='MapInfo File', symbologyExport=QgsVectorFileWriter.FeatureSymbology) from os.path import abspath from qgis.utils import iface _vlayer = iface.activeLayer() _writer = QgsVectorFileWriter.writeAsVectorFormat( layer=_vlayer, fileName=abspath("D:/test_file.tab"), fileEncoding="utf-8", driverName="MapInfo File", symbologyExport=QgsVectorFileWriter.FeatureSymbology )