HA isn’t cheap. Yes, you could buy multi sensors, but then they’d be exposed on the doors and you’d have to look at them instead of using the already installed, hidden (I assume) door sensors. You shouldn’t need power to the alarm panel. The existing door sensors are (most likely) magnetic switches, they just complete a circuit. Tying the wires into the Schlage sensors just tells the sensor whether the door is closed or not, and the Schlage sensor sends the signals to ST for you to see/use. That’s what I’ve done for my home and it’s been very successful. I’d like to consider gaining remote control of the alarm itself, but that’s not really necessary for me, so I’ll put my $$ elsewhere!
While I’ve not done it myself, from what I’ve read using a shield or arduino is just a way to gain control of the functioning alarm system…which it doesn’t sound like you’ve got. I’ve not done much of anything with arduino, so I’d be the wrong person to speak on how you might integrate those switches into a useable model. I’m sure someone on here can give more information!