As @dan-cornilescu correctly mentioned, Google App Engine automatically scales horizontally and handles the connections to your Cloud SQL instance without you having to care about.
But taking a look at your last comment on his answer :
Thank you, I understand that Google App Engine can scale dynamically
and let the created instances connect to one Google Cloud SQL
Instance, but I'm looking for a solution for the limited space and
performance on this Cloud SQL instance. Is there a way I can connect
Google App Engine to multiple instances and so increase the database
space on Google Cloud SQL?
I will go ahead and give you some options in order to address the limited space and performance of your Cloud SQL instance.
Regarding the limited space, when creating your Cloud SQL instance you can check the option “Enable automatic storage increases” under the “Configure machine type and storage” dropdown.
Regarding having multiple instances, remember that Cloud SQL instances scale vertically but not horizontally, so the first option I would recommend you is to switch to Google Cloud Spanner if what you are seeking is horizontal scalability. At the moment is the only database within Google Cloud products that allows to do so and is the choice to go.
You can also “fake out” the horizontal scalability by creating multiple Cloud SQL instances, which is indeed a best practice. While doing so, you only have to take into consideration that the amount of instances allowed per project is 40 and you will have to request an increase if you wish to have more.