Most applications/services offer mail as notification channel. Even old school unix utilities such as cron support sending mail (through the system MTA). I use msmtp. Then configure K-9 mail or any decent mail client on your phone, setup filters so that mail from your services ends up in a high priority folder in your mailbox with notifications enabled.
I want to be able to receive notifications both on mobile and desktop, this is the only reasonable option I found and have been running with it for > 10 years.