My research group "fishes data" is there anything I could do? I am a PhD student, and my supervisors have a "different approach" for doing research.  They do not dig into the literature to find a gap and then do research on that. Instead, they just do some surveys and then hand the data over to their students, who go through it in order to find an interesting research question to address. Is this fishing for data? Is there a body in which this could be anonymously reported? Or is just one of the bad practices that one can sadly find in academia, and unfortunately in this case on my PhD research?
"Fishing" is fine for exploratory analysis: formulating hypotheses to be tested. It can even be publishable if you are straightforward with your fishing: reporting data is not unethical. Fishing without accounting for your fishing, however, is quite problematic, as your question implies.

Unfortunately, in some fields it is common to go straight to publishing exploratory analyses as if they were not exploratory. Statistically, this is a bad idea; the 'replication crisis' in especially psychology is an example of the consequences. If you torture the data enough, nature will always confess.

As awareness of this problem spreads, some journals and funding agencies have now gotten very strict, for example with clinical trials, and demand that trials be preregistered to be published/funded to avoid the increased rate of false-positives from "fishing" through data. I'm not aware of anything similar in other types of research, but certainly that's the direction that statisticians would suggest to avoid reporting misleading results.

As far as what you can do, it really depends on the standards of the field, and you are in a vulnerable position as a student. I would recommend you not publish "fished" data with your own name on it unless the extent of the exploratory analysis is made clear, and that you advocate to apply appropriate statistical approaches to fished data, like using those results to inform a subsequent study to properly control your false positive rate.