I've done this before. To send text messages to my phone I leveraged a little known feature mobile providers offer. They will forward an email as text when addressed to the 'phone number' @'mobile provider.com'
Then it was a simple matter of setting up the mail command with a simple message relevant to the notification.
Naturally you need to have the device online for this.
Alternatively UDP notifications can also be used to send messages to devices on a local network.
INDI/KStars on Raspberry Pi 4, 4gb
Raspbian Buster with AstroPi3 script configuration
Skywatcher HEQ5 Pro Mount
Canon 600D Camera
Orion SSAG/ASI120mm @280mm Guide Scope
Waveshare Stepper Motor Board - DIY Focuser
Adafruit GPS Module
Generic Bluetooth Joystick.
Startech 7 port powered USB Hub.