Google cloud function and cloud sql permission

[D Kantor]

Hi , 

I'm trying to create a cloud function that writes a dataframe into a could postgresql database, but the function always timeout. On the IAM page I added a Cloud SQL Client role to the App engine default service account, but on the Functions page under permissions it doesn't show the Cloud SQL Client role of the App engine default service account. My database and function are placed in the same project.

Screenshot of the IAM page:

Screenshot of the Function/permissions page:

What am I doing wrong?

[Andrés Márquez]

Can you refer to these[1][2]? Is it helpful?

[1] https://stackoverflow.com/q/71507095/15774176
[2] https://stackoverflow.com/q/64100523/15774176