The original AL-41F engine was supposed to be used in pairs on the MFI aka MiG Project 1.44 and as a single unit on the LFI.
You usually do not define engine generation by either size or thrust but by thrust-weight, turbine inlet temperature, and things like that.
The AL-41F was a variable bypass ratio engine, so it was in fact technologically more advanced than either the F-22 or F-35 engine and more similar to the GE engine used in the YF-23. The turbine inlet temperature is similar to that of the F-22 engine and the thrust-weight is better and closer to the F-35 engine.
The AL-41F was large because in order to fullfill the missions required by the Russian defense ministry with the single engine aircraft back then they needed more power than could be done with a smaller engine. The AL-41F engine prototype first flew on a MiG-25 which is an aircraft with much larger engines than a Flanker.
Anyway the project got cancelled and the engine never got properly finished, never got certified, and never entered serial production. They made several prototypes for testing including flight testing but that was about it.