Help Engine shaking and abnormal noise are not EGR problems

I bought a used car and drove it for two months. Recently, when I got off the highway, the engine started to shake and creak at idle.
The noise stopped when I stepped on the accelerator, and I drove home at 40 miles per hour.

I thought it was a common EGR problem, but when I opened the EGR valve and EGR cooler, they were very clean. It was obvious that they had just been cleaned not long ago, but there were some oil stains on the small EGR pipe of the intake manifold.

After cleaning the intake manifold, I thought the problem was solved, but it still shook.

I found that the cold start was normal, and it would run normally during the warm-up phase, and then it would start to shake after a minute or two.

When I went out for a test drive, it would also shake when I stepped on the accelerator. Note: when the problem first occurred, it would not shake if I stepped on the accelerator deeply.
NOTE: When the problem first started, if I pressed the accelerator deeply, it would not shake.

Also, when the idle shake occurred during driving, the engine would stop shaking when I stepped on the brake, and it would run stably just like a cold start.

Also, after the warm-up is completed, it will return to normal and not shake for a few seconds before it is about to shut down the engine.

This is really strange. Is the Prius brake still a vacuum assist system?

Is the warm-up load to charge the high-voltage battery heavy? The engine will shake

What is the logical relationship here?

Request guidance

It's like being Sherlock Holmes