Gen 4 engine issues?

I haven't experienced anything like that in our 2017, but it only has 23k miles. What is the odometer reading on your car? I'm assuming you aren't getting any trouble lights or messages on the dash. Possibly you could take it to a Toyota dealer for a ride-along, but if there are no trouble lights you wouldn't be able to get any warranty coverage, so you would have to pay for a diagnosis.

 

Bad gasoline? Water in the gasoline? Try some Heet gasoline dryer maybe. Any effects noticed at idle? You also might want to remove the plastic decorative cover on the top of the engine and trace out the connectors and cables from the harness to the fuel injectors and the spark plug coils, and look for any other obvious damage to the wiring. I think Toyota still uses an insulated wire made with soy protein or some such that rodents like to eat. Lastly, consider a dealer diagnostic.

 

I believe I know what you are talking about. It DOES feel like its shuttering but it is just very low RPM being driven by wheels. Get a scangauge or a basic bluetooth dongle and connect it to an app called torque to see what RPM's this is happening on. Mine is usually like 992 or something like that. I used to have a manual prior to my prius and the manual felt the same exact way when running ultra low RPMs. As far as loosing power upon take off, are you maybe hitting some kind of bumps possibly, it does decrease the power when hitting a bump, man hole cover, ect for traction control purposes

 

If you had this with your previous car then it points to what @AzWxGuy says in his first sentence, contaminated fuel. I would run it low then fill up with fresh, Premium branded fuel from a different gas station.