3rd party mobile app to notify of battery charge level?

Nothing I have read or heard exist. The Remote Connect which is not available for 2020 PP was available for pre 2019 Prius Prime Advanced as a Prime App, which would have given you the ability to check the traction charge status remotely. As you found out, this app no longer works on 2020 or newer PP. In order for the third party app to work, it has to utilize the car's telematics or have it's own telematics and have ability to communicate to the car's ECU on charging status while the car is off. That alone is very high hurdle for any developer of app to jump.

One possible way to monitor the charging remotely is to use some type of smart plug with energy monitor function on the wall side with enabled WiFi or Bluetooth connectivity to your phone app. It will not show you the traction battery charge status, but it will show you electric draw over time, so you can infer from it, if the charge cord is removed and the charge interrupted, or charging in progess, or the charge completed after ~5.5hours. You just have to find a smart plug that is rated at high enough to support at least 12A or higher of constant draw. Most sold now say rated for 15A, but may fail over time due to poor QC. Depending on the location of the wall receptacle, this smart plug may also have to be suitable for outdoor use. However, I am not aware of any smart plug with energy monitor function that can be used outdoor. I use several models of smart plugs to control and monitor energy use of electric appliances in my house, but they are for indoor use only, and differently not for 12A constant draw of 5+ house every day.

Edit: This outdoor smart plug claims to have an energy monitor functionality. There maybe other outdoor smart plugs if you look for it.

A few more I found:
http://www.amazon.com/Monitoring-Function-Koolertron-Individual-Compatible/dp/B07ZVMX2F6/
http://www.amazon.com/Etekcity-Outdoor-Remote-Control-Outlet/dp/B07JB5TQSG/
http://www.amazon.com/Outdoor-Compatible-Outlets-Waterproof-Monitoring/dp/B07QJWGRYB/