Trying to share my thoughts for future visitors
Let me start with the below image and then we will see the OP's questions one-by-one:

As far as I can see, GKE seems to be slighty more complex to configure
and deploy an application (using Kubernetes direct files or Helm
Charts or something else ?).
When you see from the perspective of a client who does not want the overhead of managing the environment - basically a PaaS client - then, yes, Google Kubernetes Engine is slightly more complex as compared to Google App Engine.
As you can see in the above diagram as well - GKE is more towards the left, which it is a less vendor-managed cloud solution, so environment configuration and management overheads are expected.
Furthermore it seems to have no better pod failure detection or better
performances ?
I have not used Google App Engine but I can assure you that Google Kubernetes Engine is a certified Kubernetes (check more over here) so if you are running Kubernetes on Google App Engine, you can be sure that GKE is offering you same performance and features as Google App Engine.
Why should we use GKE whereas there is GAE which only needs
dispatch.yaml, app.yaml files and gcloud cli to deploy ?
As I mentioned in the start and as you can see in the above diagram as well that it is all about control over the environment - the more control you want over your environment, you will select a solution farther on the left side. And please note that more control means more overhead of environment management, and exactly that's the reason why people tend to choose solutions from farther on the right side.
Is there any technical or financial feedback against GAE ?
Both Google Kubernetes Engine and Google App Engine are highly successful and production-grade offerings from Google, so you can be sure about technical aspects. For financial aspects - you need to check their pricing model and see which will go more smoothly in your pockets.
Finally, how can we make a choice between GKE and GAE ? What whould be
the reason to not choose GAE ?
IMHO - the top three decision points could be:
- How much you control you want over your environment
- More control comes with more self-management, so are you ready to go through the overheads of a self-managed environment
- Your budget