On the issue of bug counts, there was one huge study, that was successfully reproduced [0], which finds that there is a real but small negative correlation between FP and bug counts in large GitHub projects.
For productivity I haven't been able to find any large-scale studies that compare functional vs imperative/OOP languages. I did find one small scale study [1] that found significantly better productivity for Haskell (and a Lisp dialect) vs Ada, C++ and a few others, but it was about a specific small prototype problem with just a handful of programmers participating (the Haskell program had 85 lines, the worse, C++, had 1105; and programs took between 10h and 54h to finish - hardly representative of large-scale coding). Most other studies on productivity that I could find [2], [3] didn't include any FP languages at all.
[0] https://arxiv.org/pdf/1901.10220.pdf
[1] https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36...
[2] https://www.e-informatyka.pl/attach/e-Informatica_-_Volume_1...
[3] https://www.researchgate.net/publication/4261726_Do_Programm...