Hi,
A backfire can be caused by several things. The fuel mixture can be too rich or lean, a vacuum leak can cause problems, engine timing, and so on. Take a look through this link.
Since you have no codes, I need you to check a few things for me. First, if your scanner has live data, check the signal from the engine coolant temperature sensor. If it is sending a faulty signal, the computer will overcompensate to meet the needs. For example, if the ECT indicates -40 degrees F and the temperature is actually 75 degrees F, the fuel mixture will be too rich and can cause this. Plus, the PCM only knows it is getting a signal. It doesn't know if it is correct.
If that checks good, start the engine and while it is at idle, check the short-term fuel trims. Let me know what they are.
If you haven't already, confirm there are no engine vacuum leaks.
https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge
Although the fuel pump has been replaced, the regulator could be faulty, so it is a good idea to confirm the fuel pressure is within the manufacturer's specs. Here is a link that shows how to test pressure:
https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator
Pic 1 below shows the fuel pressure specifications.
Also, when it fails to rev, pay attention to the tachometer to see if it drops to 0 when it happens.
One last thought, are there any odd sounds from the exhaust system? This type of issue could also be related to a plugged catalytic converter. If nothing else helps, remove the two upstream oxygen sensors (pre-cat). This will set codes, but you will be able to tell if it is running better. The removal of the sensors allows an added place for the exhaust to be released from before the converters. It isn't a normal amount of flow, but it usually is enough to tell a difference.
Let me know what you find or if you have other questions.
Take care,
Joe
See pic below.
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Tuesday, January 25th, 2022 AT 6:30 PM