As was mentioned in @nr_aus's comment it is possible to edit the ESRI File Geodatabase since QGSI 3.22, see the changelog for more details.

I test it with the following data file: https://gisdata-piercecowa.opendata.arcgis.com/datasets/1ed55090838643a99b07fdffdb0e5ac9_0

And similar code as above will work:

from os.path import join
from qgis.core import QgsVectorLayer

working_folder = "C:/Users/taras/Downloads/Libraries_9209718161064393263/"
fc_Opt_Prospect = join(working_folder, 'f49bdce3-128c-4082-9beb-71ab798f7410.gdb|layername=Libraries')

layer = QgsVectorLayer(fc_Opt_Prospect, 'Libraries', 'ogr')

with edit(layer):
    print(layer.isEditable()) # True

Tested on QGIS 3.34.6-Prizren on my Windows 11.

As was mentioned in @nr_aus's comment it is possible to edit the Esri File Geodatabase since QGIS 3.22, see the changelog for more details.

I test it with the following data file: https://gisdata-piercecowa.opendata.arcgis.com/datasets/1ed55090838643a99b07fdffdb0e5ac9_0

And similar code as above will work:

from os.path import join
from qgis.core import QgsVectorLayer

working_folder = "C:/Users/taras/Downloads/Libraries_9209718161064393263/"
libs = join(working_folder, 'f49bdce3-128c-4082-9beb-71ab798f7410.gdb|layername=Libraries')

layer = QgsVectorLayer(libs, 'Libraries', 'ogr') 

if layer.isValid():
    with edit(layer):
        print(layer.isEditable()) # True

Tested on QGIS 3.34.6-Prizren on my Windows 11.