You don't need to publish a new paper to introduce reasonable doubt about the conclusions of one observational study that contradicts long-standing policy in numerous areas. Just look at the limitations of the paper itself, which is freely available, as are the well-known primary data sets on which it is based.
Unlike most of the media reporting over the past few days, the original authors do acknowledge numerous factors for which they could not or did not control right there on the front page of the paper under "Introduction" and further in an extensive "Limitations" section later on. Some of those limitations are quite fundamental; here are a few things this study didn't or couldn't take into account:
1. The crime data set they were working from did not distinguish between day-time and night-time crimes.
2. The crime data set they were working from did not provide precise location data so it was only analysed within larger areas. Those areas could have had multiple street lighting policies in effect in different locations within them.
3. The STATS19 data set they were working from is primarily about motor traffic and only covers reported incidents. It provides limited insight into the causes of injuries to pedestrians or cyclists unless they directly involved a motor vehicle and resulted in police action. It appears that the study also considered only fatal and serious injury incidents, not minor injury incidents or those causing only damage to property.
4. Neither data set controls for confounding factors, even obvious potential distortions like general improvements to road safety being implemented at the same time. During the periods when lights have been switched off near us, for example, we've also seen speed limits in residential areas widely reduced to 20mph and various safe cycling schemes affecting local road layouts. It is not possible to separate the effects of those different schemes based only on the STATS19 data that appears to have been considered in this study.
5. Both data sets provide only absolute statistics. Neither data set accounts for relative effects like fewer people going out late at night if the lights are off, meaning fewer people to be the victims of certain types of crime or involved in road accidents.
If you genuinely want to know more about this issue, I encourage you to start by reading the original paper. Here it is. Also read some of the opposing commentary by councils that have reversed decisions on this policy after trying it and then seeing their own specific data, and road safety groups like the AA that also analyse STATS19 and other experimental data and have previously reached very different conclusions about the effects of changing street lighting. Many of these sources are also publicly available and yours for the price of a few minutes with your web browser and search engine of choice.