According to the ÖAMTC (Austrian Automobile Club), no Ukrainian car is currently penalized, but officially every car should have a vignette if it wants to use the motorways. The purchase of a vignette is therefore recommended. Tip: Your mentor may be willing to get one for your car.
According to our own experiences at the border with the Czech Republic, if you want to pick someone up, you will get confirmation from the petrol stations near the open borders, where you can also get the vignette, that no vignette is necessary if you are picking up Ukrainians.