help needed - 06' Yaris YR power loss on freeway

[roc]

Hello,

I bought this 2006 yaris YR 3-door hatch with 143,000 kms on the odometer last week from a used car dealership and I am having some annoying power issues

During test drive everything was fine, but then right after I have paid for the car and was driving back home on the freeway doing about 90 km/h, the engine started shaking, car started to lose power and could not go anything faster than 30 km/h. None of the warning lights lit up on the dashboard when this happened.

I pulled over and immediately called the dealer about the issue, and he told me it was because of bad fuel clogging the fuel filter. He asked me to switch off the engine and wait for half an hour for the impurities to settle which I did, and the car started going again and could do about 60 km/h, but the engine was still chugging when the car was idling, as if it would die in any second.

Car was low on fuel so I pumped premium fuel into the tank and slowly made my way to a mechanic who is a friend of mine. He did a check for me and measured low fuel pressure. Thanks to statutory warranty, I took the car back to the dealership and had him replace the fuel filter and fuel pump for me, but then the same thing happened again on the freeway and this time I could smell something burnt in the engine after I opened the hood.

TL;DR, to summarize:
- Car was fine before going onto freeway;
- Car starts to lose power after doing about 90 km/h on the freeway for a while;
- After power loss, car could not go anything above 30 km/h even if I floor the pedal;
- Car started going again after I turned off the engine and waited for half an hour;
- Engine was shaking and chugging when car was idling as if it was going to die in any second;
- Quick check shows low fuel pressure;
- Replaced fuel filter and fuel pump but problem persists;
- Burnt smell from engine after I opened the hood.

What else could be the cause of all this other than fuel pump and fuel filter? Thank you very much in advance for any insight that can be provided on this matter!