knocking and surging

have you cleaned the egr circuit?

 

How long have you had it?

 

Coolant level?


I was thinking 'Prius Death Rattle' but that's usually a symptom that goes away while you're driving.

Knocking can be looooots of things like: a motor mount, a cylinder knock from an incorrect air-fuel mix, water from the coolant loop getting into the engine, and all kinds of other things in a car that is basically at "end of life."
Most 'knocking' is bad....
Sometimes it REALLY bad.
I'm thinking that your mechanic might be incorrect about "switching between gas end electric modes" because a wireless G3 (non-plug-in) is always in "gas mode" at 35MPH.
Your "transaxle" which is actually called a 'power split device' that uses Motor Generators to charge the traction battery, start the car by spinning the ICE, and to drive the wheels or assist the ICE by providing additional power - on demand.

I can see MG2 maybe causing the symptoms you are describing - and it's an easy fix!
Just replace the [sic] transmission.

I'm a little bit of a hard sell on this being the culprit though.
You never mentioned what your mechanic wanted to do about it?

 

Has ALL maintenance been done in a timely manner? Full synthetic oil changes? What is the normal operating temperature? Was the electric water pump ever changed? Have you ever put injection cleaner in your tank? Are the motor mounts intact or been checked?

 

Has it done that the entire time you've had it?
Possibly coincidental, but that's around the speed at which mine is indecisive whether to run on battery or engine power.
There is no literally noisy switch..

 

So the eCVT transmission has never been serviced? With other types, with high-mileage, folks advice not to mess with it as it can cause issues but I haven't heard that on the eCVTs on Toyota's so might be smart to get that VERY old transmission fluid changed out. (It's almost as easy as an oil change so shouldn't be too expensive.)

 

Check the air filter; clean the MAF and throttle body. Also check your vacuum hoses to see if they are brittle or leaking. I'm not sure if they've been eliminated on a 2014. I believe there's a motor that controls the throttle body flap. If that's malfunctioning; that could choke-off air to your engine; resulting in the bucking.
I would also check the gas pedal - It's a DBW (drive by wire) setup. The ECU isn't going to trigger an error; if it thinks that your "pumping" the gas pedal - gas pedal data is staying within range; even though it's actually malfunctioning.

You just need to be smarter than the computers; when there's no CEL.

 

Taking the position its too old to maintain properly means you have the wrong car.

I would do the egr block flow test. Not much work and zero cost. Could point to an egr valve that is not closing properly and effectively acts like a vacuum leak at low rpms. Toyota has a revised egr valve and software for the issue.

Start with no cost egr block flow test
https://youtu.be/lFVNaDJ6HOI?si=lZjJK932oimbrx8R&t=238

At about 10:15 in the video he starts talking about the egr valve letting "air" into the intake manifold. He means exhaust gasses. A blocked egr cooler won't cause death rattle or misfire codes. A sticking open egr valve can cause rough low speed engine operation. Both will normally cause an egr code but low cost scanners may not pick it up. Neither will cause loss of coolant.