Looks like heat damage from the oven. The drawer front looks like a vinyl wrapped panel, so the plastic coating has just gotten too hot. If you've used the oven normally, then it's perhaps fair wear and tear. The drawer front must have gotten fairly hot for it to bubble like that which might mean that the door seal on the oven isn't great. The cause needs addressing first before trying fix the drawer front, otherwise it's just going to happen again. Increasing the gap between the drawer and the oven will help.
If I was the landlord I'd want to know so I could stop it getting worse, or so that I could try and get a new panel before they were discontinued.
I think it would be difficult to repair but if a replacement can't be found, it might be possible to swap the panel with another one where the damage is less obvious, against a wall for example. An alternative would be to edge the drawer front in something heat resistant, like an aluminium strip.
Updated to add: I think I can see a small opening in the centre of the damaged area on the oven casing. That might be a hot air vent; the air is pushed out of there and forced along the edge of the drawer. It might be instructive to find the fitting instructions for that oven and check the clearances / advice notes for the vents because the oven may have been fitted incorrectly. That would reduce your culpability here. Check the right hand side for damage too.