How is the fuel consumption of the 1.6T Ultimate Edition? Are there any common issues?

In winter, after ignition, the car feels a bit shaky for the first 1 or 2 kilometers, and the engine sounds a bit rough. The service center mentioned that it might be time to replace the timing belt or timing chain. It's a 2015 model with 62,000 kilometers. No other issues.

Common issues, I'll mention two I've encountered: engine fault warning, replaced the turbocharger blow-off valve. The engine burns oil, but doesn't report low oil within a maintenance cycle; less than 1 liter of oil is drained during maintenance. Electrical fault warning, but it doesn't affect driving, so I was too lazy to check. The Varta yellow label battery that I've used for over four years is dead, not sure if it's related to the faults.