Your linked research has 'Eat a plant-based diet' as a High Impact Action, not a Moderate Impact Action.
You asked for evidence that a plant-based diet is one of the most effective ways. You found it.
Also I already don't own a car at all and I haven't taken a plane in a little over a decade.
The study gives everyone a 2.1T emission budget per year in order to achieve the 2 °C climate target. A single trip by plane can produce more than that, as can buying the wrong kind of energy. A EV car alone produce around 1T per year. A meat-based diet can coexist within that budget, same as the EV car. The average win for switching your utility purchase to a emission free source is 1.6T, while switching to a vegan diet is 0.8T. That illustrate the effectiveness between different kind of strategies to stay within that 2.1T emission budget.