Yep with most people having data plans or local Wifi certainly a app notification service would be more cost effective.  Locally in NZ our cost is an eye watering 10c per sms but for our company we only do 1200 to 1500 per month.  Just looking at twilo cost now, so at 0.0078 sms per 88k, yeah $695 per month, ouch.
In the past I've looked at alternatives but not bothered to go further since our clients pay for their usage at present.  I did look at ntfy.sh which is opensource with server self hosting or paid service.  Not sure if you can have private topics through the paid or not but self hosting allows ACL type user password.
For viewing they have website integrations but has an App that can be used for both Android and Apple.  I have to say for your own app it could be created but I've found Apple is the biggest pain in the room where you have to pay them for developing per year (not huge cost there) but to compile requires Apple hardware which is constantly needing software updates and being Apple they get to 3-5 years old and decide no you can no longer upgrade the hardware mate.  You must buy some new hardware to compile on now.
Just my experience in this though.  I've not bothered with the stores though, as just an Adhoc type app for limited clients.  Apple is super restrictive so looking to go more webapp style.  So ntfy's app looks to be that style option as well which has a website backend as well I believe.