Code will demo conceptual model:
Driver -> Data Source -> Layer -> Feature -> Geometry
Multiple options for reading FGDB's...
comparison of opensource vs esri driver
import osgeo.ogr as ogr
driver = ogr.GetDriverByName("OpenFileGDB")
...
dataPath = r'./data/BCTS_OPERATING_AREAS_SP.gdb'
# proprietary ESRI driver, read only, requires separate install
#driver = ogr.GetDriverByName("FileGDB")
# opensource driver, use this! DS is a DataSource object
driver = ogr.GetDriverByName("OpenFileGDB")
ds = driver.Open(dsath, 0)
...
...
layer_name = 'WHSE_FOREST_TENURE_BCTS_OPERATING_AREAS_SP'
lyr = ds.GetLayerByName(layer_name)
...
...
feat = lyr.GetNextFeature()
...
...
geom = feat.GetGeometryRef()
area = geom.GetArea()
...