I couldn't find an Overcooked 2 speedrun after a cursory search on KZfaq, so here you go. Single segment. Run starts at 0:00:22, when I hit new game, and ends at 3:25:45, when it fades to black to go the credits.
3-star speedrun is defined by getting 3 stars on every level, including the 8 Kevin levels. This is 135 stars over 45 levels: the tutorial level, 36 main levels, and 8 Kevin levels.
This was my first attempt, and it was more of a casual speedrun at best. Lots of mistakes to clean up here. First of all, I didn't even notice it was possible to skip the minute-long cutscene at the start.
Since most of the levels are a predetermined length, the only time you can save on anything except the final level is skipping text and maneuvering the overworld faster. In the final level, however, I predict it's possible to beat it in 10 minutes if you're very quick. At the end I waste at least 45 seconds accidentally baking a pancake instead of cooking it on a stove and I had to start over that recipe.
A sub 3:20:00 run is probably possible, but since most of the game is on extremely specific time limits, you probably won't get much less than that.