Ntfy can act as an email server if you configure it. So if an application is not supporting ntfy directly but email, you can go that route. Ntfy will then simply forward the email as push notification. Its also pretty simple to set up, used this as a workaround because authelia doesn't support it directly. Here is the link to the specific ntfy documentation: https://docs.ntfy.sh/config/#e-mail-publishing
I used the local variant (https://docs.ntfy.sh/config/#local-only-email) which does not require any DNS entries, as I only use it for sending notifications between my self hosted containers (all on the same host).
If your router allows it you can set your gateway IP from the router (i.e. 192.168.1.1) as the second DNS address in the DHCP settings. So your routers DNS settings would then act as fail over in case your pi-hole is down. That's at least how I have done it on my ISP router.