Hi, Yesterday I received this e-mail by Google:
We’re writing to let you know that starting June 20, 2024 the legacy Firebase Cloud Messaging (FCM) APIs will be discontinued. On June 20, 2024, we’re reducing the number of Firebase Cloud Messaging (FCM) legacy register APIs and legacy send APIs that provide similar functionality. This step will allow us to provide you with a more consistent experience and align with Google security standards to improve security, reliability and performance. Because of these API decommissions, some already-deprecated SDKs and features will stop working after June 20, 2024

Is the project parse-server-push-adapter somehow affected by this interruption of support?

You are correct that this will have an impact on the push adapter, see