Proton is motivated to replace Google products with privacy respecting solutions, however the Android app uses Google's FCM. While this is the easiest and most efficient way to receive push notifications, there should be a replacement (UnifiedPush or a own service, as requested in other ideas).
Until this is considered, another solution could be polling every 15/30 minutes (Thunderbird works like this). If the downsides like delayed notifications and slightly increased battery use are communicated to the user, this would be a good improvement for devices without Google Play Services.