Assuming the tablet is running Android (though just as easy on Windows), use an automation tool to do something to keep the tablet alive. Also you should automate the browser to reload the page occasionally which should help reduce issues. Changing tabs on Dashboard isn't enough as all of that is in memory.
Also remember that the Dashboard uses both Angular v1 and JQuery libraries which makes the browser page very large. If you really want something that runs 24x7 I would recommend using a dedicated app or a lighter weight custom webpage dashboard.
If availability is very important - which is apparently the case for you as you need to be able to switch off the alarm within 20 seconds - I would be very careful with handcrafted solutions. The tablet option in that case seems a no-go to me as it would add extra complexity and a proper 24x7 stable dashboard solution is not known.
Regarding the pi with TFT touch screen option: I certainly would go through a lengthy test phase before putting this into production. Switching on/off your alarm system is not the first IoT use case I would recommend.
specifically for the alarm and daily use after several test I moved to an RFID reader which is the most easy solution even I made the keypad with node red and still have it.
For android there is also a specific app for a MQTT alarm panel which works well:
And if you plan to do a dedicated panel with a raspi and a 3,5" display there was an interesting prject here:
As told, in my case I integrated the keypad directly on node red but I'm using the RFID for simplicity, cost is around 5$.
I'm not an Android person so probably not the best person to ask. But I believe that most people use Tasker for Android automation. You may well find some settings hidden away that will let you keep the device on as well. Certainly I have my old iPad set to never turn off as I only read RSS news feeds on it these days.
A Google search turned up some possibilities for browser automation. But it is easy enough to get a web page to reload itself periodically.
On Android, under Developer options there is a Stay Awake while charging function.
You can enable the developer menu by opening the "about phone" menu and pressing the "build number" tab 7 times.