It might be understandable if it cracked as soon as you lit it. Possibly reaching a high internal temperature before the glass had properly warmed up externally.
I can't think of any reason why it should crack overnight, while the stove is shut down and just "ticking over." I can only guess that it was pure bad luck.
Treated glass is under massive internal stress even while it's just sitting there. My front door exploded on a hot Summer's day a couple of months ago. No reason. I guess that, with your stove, the doorframe simply expanded at a different rate from the glass.
I would replace it as soon as possible. With the controls opened up, I doubt if there is much danger. Shut down overnight is rather different. The gases have a very small opening in which to escape. If the crack opens, CO might well escape.
A simple CO detector is always a good safeguard in any case.