Is there any proprietary Android app for which you wish there would be an open-source alternative?
Basically, what the title says. Do you use any app, that is proprietary, but either has no OSS alternatives or they're all not good enough? If there is an alternative, what keeps you from switching?
Molly FOSS and Molly with UP replace the Google's notification system with websocket and UnifiedPush respectively for its own notifications. Google (hopefully) doesn't have access to all notifications you get on your phone but only to those sent to apps that utilize their push implementation which Molly doesn't use.
Afaik Signal servers have nothing to do with it. There are 3 possible situations depending on what app you choose.
Official Signal app. It asks Google to check Signal servers for notifications and to send them to you if there are any.
Molly FOSS. It connects directly to Signal servers without any push middleman.
Molly UP. It asks the push notifications provider you choose (but not Google) to check Signal servers for notifications and to send them to you if there are any.
Ultimately, it's the apps and not the servers who decide if they want to use Google's services or not.
Official Signal app. It asks Google to check Signal servers for notifications and to send them to you if there are any.
I don't think that's how push notifications work. It would not be instant, and very frequent polls are very resource intensive, even more if you had to do it for the servers of a million different apps.
UnifiedPush has a diagram here, and the popular proprietary push providers should work the same way too.