I think in principle if you have enough resource, and investigate the right fine tuning techniques you can get the SOTA out of them. However, at the moment it's quite new, moreover not as open access for research. Furthermore, RL training is not easy to do for a random researcher (because it's kind of in a human in the loop framework and you require human annotations --- you can kind of probably do it with AWS and such though; but it probably won't easily become a standard too soon because of the inconvenience).

Another thing is ELLM (let's say "extra large language models" to distinguish GPT3+ style of models from BERT/BART/Roberta/GPT2 style of models) are generally used in few-shot setup/instruction following setup, and probably won't fit exactly with "fine-tuning on whole dataset" setup. And it can be again hard for random researchers to fine-tune or even run those humongous models. So it may again take time to time to seep into everywhere.

In my investigation ChatGPT seems to still struggle a bit on some harder logical challenges (some of which even I struggled a bit with) eg. in LogiQA: https://docs.google.com/document/d/1PATTi0hmalBvY_YQFr4gQrjDqfnEUm8ZDkG20J6U1aQ/edit?usp=sharing

(although you can probably improve upon by more specialized RL training for logical reasoning + multiple reasoning path generation + self-consistency checking + least-to-most prompting etc.)

I think SOTA of logiQA is: https://aclanthology.org/2022.findings-acl.276/ (you can find relevant papers by looking at the citation network in semantic scholar)

For reasoning on other areas, you can probably use the chain of thought papers and its related citations to keep track (because COT is almost a landmark in prompt engineering for enhanced reasoning, and most future ELLM paper working on reasoning would probably cite it).

Don't know much about common-sense reasoning (either as a human or in terms of research in that area).