Gen 2, Cold shift ruffness / stutter (not ICE kicking on/off)

I have a 2007 with 135K miles with conservative driving practices. I have notice in the last 3,000 miles or so that I have a ruff shifting at low specs (guestimate is say below 25mph) when the engine is cold - overnight or when I do not drive it for a few days. Once the engine warms it smoothes out. Just to clarify I am aware and know the difference between the ICE kicking on and off and this is different. The symptom came on abruptly when it started 3,000 miles ago with no noticable lead up to it happening. I am running on the original transmission fluid - I knew there are all different views on this and Toyota calls it a "lifetime fluid" but does not define "lifetime." ICE Oil is changed every 5K miles with Fully synthetic 5w/30 located in Southwest Florida. I swithed to fully synethic probably about 10K miles ago. I have scanned it with my Actron CP9575 scanner and no codes at this time.

Any thought on where I should start trouble shooting? O2 sensor? Transmission /(transaxle) whatever it is, lol. etc.

Should I start by changing the transaxle fluid? (ATF WS, 4 quarts needed per Patrick Wong post)

I am getting ready to do some preventative maintenance myself: all struts and coils, ICE 3 way coolant control valve, new tires, etc and before I put money into this I would like to first fix or ID the cause of the shifting stutter to rule to a transmission issue/failure.

 

Thank you for the clarification. That is great to learn and takes the focus off the transaxle. I just returned from driving about 10 miles and the car was already warm as I drive earlier this morning. Once the engine is warmed the problem is minimal and erratic at best and the feeling is barely noticeable and inconstant. The issue presents like the ICE kicking on and off but I am really struggling to accept that because it "feels" different as I have owned the vehicle since 2009, however, I can be open minded to the idea of it being the ICE engaging or disengaging.

To answer the question of fee/ hear/ etc. There is no sound it is a feeling which is difficult to describe. It is a vibration.( stutter, bumpiness, choppy feeling) for 1 to 2 seconds when the gas petal receives slightly more pressure to accelerator and it also happens when the gas is released. It seems to happen below 35mph which I know is around the cut off for the electric motor/gas combo. When I apply or let off the gas petal is a very slow and gradual release or application of the pedal and the stutter occurs at this point.

So, to try and pinpoint the characteristics of the issue as requested I will report back in the morning after a cold start when it presents the worst.