The glass is held in by a foam\rubber seal, as it needs the ability to move flex as the metal surround gets hot it expands.
My suggestion would be to use something like plumbers mate, or something like that to help secure it while still allowing some give.
Plumbers mait is like a putty, you normally use it to support bathroom sinks etc, it has a high flash point so should be ok on cookers. A silicon \ sealant probably would burn (Im not aware of any which can withstand 200 degrees.
For example screw fix sell it here, you get different types I would always put some on a metal spoon and hold it on a few layers of tin foil then place it on the hob to check it doesnt fail after 10 mins of medium heat, to be fair the temp on the outside of the glass wont be more than 100 but its worth checking, rather than finding out it crumbles and dries out the first time you use the cooker.
Yes I would remove the hob frame holding the glass in place, put the putty a few mm thick where the frame secures the glass, then compress it, secure the hob top back in place, remove any excess and check the glass doesnt slip. As its putty there is no setting time it should hold it in place while giving some give.
OK, it sounds like the part comes as one piece which is the glass and metal frame (normally the frame and glass are separate).
The tabs are clearly taking the movement \ expansion from heating up so you dont need to worry about using putty, just securing the tabs on the glass and on the frame.
I would suggest you use a special epoxy, I have use the product here previously to fix a similar problem on a over door where the glass came away, do not use generic epoxy as it wont hold up to the heat.
Please let me know if you need any further guidance.