This looks like a relatively recent (probably less than 25 years old) oven. That being said, depending on what is wrong with it, replacement may be the best solution. Since the control panel does light up, it isn't totally dead.
In any case, combination cooktop/oven is very common but is not "modern" in any sense - both cooktop/oven together and separate have been common in the US for a long time. It comes down to personal preference. My house had separate, but both electric, but I kept them separate when redoing my kitchen so that I could switch to gas for the cooktop while keeping the oven electric, and eventually replacing the single oven with a double oven. Single ovens are readily available (subject to general supply issue affecting everything lately) and a straight replacement should not be a problem. The main issue is the dimensions - height and width of the cabinet. (Depth is almost always based on 24" deep cabinets in the US.) I'm not sure how standardized the heights are. Widths are typically 24", 27" and 30". Secondary to that is color - most manufacturers offer black (as you have), white, almond/beige/biscuit and stainless steel. And then you pick features: self-cleaning and convection are probably the most popular major differences between models - your current oven has both of those features.
Power supply is important. Your existing oven uses 3.4kW in a 240V installation. That's only 15A, so the circuit could be as small as 20A. Check the breaker to see what you actually have, as a new oven may need a larger circuit.