So I saw a article by BMW where they tested a old e36 for what is the best driving style for fuel efficiency and they saw that driving with a heavy foot, but shifting quickly at low rpms (2k) is better than accelerating slowly up to speed.

In theory this does make sense, since the engine is at its most efficient at full throttle right?

So I wanted to test this in my own car (1995 VW Jetta 3) but i thought isnt this lugging the engine a lot.My rpm dial doesnt work so im going off of feel through the pedal and then speed, shifting to 2nd at 20km/h, 3rd at 30km/h, 4th at 40km/h and 5th at 55ish.The only time i really feel something that could be lugging the engine is if i shift to 5th before 50km/h

Is this lugging my engine enough to really damage it making the fuel I theoretically save (i havent finished my test of how far I get with the slowly accelerating test) not worth it?