Characteristic value not updated during connection

[DavideSit]

Hello,
we are writing a project in order to test a mobile app developed by our company.
This project creates a peripheral device that has to expose some services and characteristics that the app needs to read.
As of now, on the mobile phone we are using nRF connect instead of the app for test purposes. We are able to properly overwrite a characteristic value from the device. However, if we try to modify such value from within the code while the device is connected, nRF doesn't see the updated value.
We are sure that the modification happens locally. In fact, if we modify the value before connecting, nRF reads the modified value.
According to a common BLE behaviour, we would expect that the modification of a characteristic value should be accordingly updated on the central device while it is connected.
Is there any option or configuration that needs to be set in order to achieve such behaviour?

Thank you.

Ps: I am attaching an excerpt of our code where the connection is defined (I had to modify the format from .py to .txt).
connection_manager.txt