Growth rate oscillation in the a population of non-interacting bacteria
The theoretical article concerns growth rates of single cells. There are many studies that model cell cycle as a non-linear oscillator (see Tyson and Novák, 2015). 

However, growth rate measurements in microbiology are usually done on cell populations consisting several cells. You generally do not observe any oscillation because:


Cells are not synchronized
There can be variations in growth rate of different cells because of noise
The measurement time points are much larger than the period of oscillation


Some of these reasons are already mentioned in the paper you linked (Jafarpour, 2019).

I do see some ups and downs in the growth rate in my own data; E. coli growing in LB in a 96 well plate.



X-axis is the time in seconds; measurement was made every 15minutes. Y-axis denotes difference in OD between two consecutive measurements. The different colors are biological replicates. However, I cannot say that this is the kind of oscillation that Jafarpour talks about. It appears more like stochastic fluctuations in growth rate or measurement errors (they are also not damping by the end of growth).