I'm having difficulty finding the maximum temperature rating of the i7-6700K. It's not mentioned on the Intel Ark web page I visited, nor is it stated in CPU-World.com, as far as I can tell.
There are numerous postings on Tom's and Reddit about safe overclock temperatures for the i7-6700K. Some people say up to 90C is OK, other's prefer 80C max.
https://forums.tomshardware.com/threads/overclocking-i7-6700k.3632005/
This stress test on an i7-6700K (presumably not overclocked) reached a peak temperature of 73C.
https://www.tomshardware.com/reviews/skylake-intel-core-i7-6700k-core-i5-6600k,4252-11.html
The Intel TDP rating of your CPU (not overclocked?) is 91 W.
The Intel Thermal Solution Specification of your CPU is PCG 2015D (130W), (not overclocked?).
Hence, at the very least, as far as I can tell, you should be using a cooler rated for 130W at stock settings. I don't know how much power the CPU is dissipating with your overclock, but it might be more than 130W. Try running CPUID HWMonitor (or similar) and see what the CPU power readings are.
Looking at your heatsink and bearing in mind only one fan is working, I'd personally upgrade to a much bigger dual-tower dual-fan cooler such as the Thermalright Peerless Assassin 120 SE. The extra mass, two more heatpipes, increased surface area and two working fans should improve temperatures.
https://www.amazon.com/Thermalright-Peerless-SE-Aluminium-Technology/dp/B09LGY38L4?crid=SJKN0Y20SQBY&dib=eyJ2IjoiMSJ9.YN_3StAsrQbqu08qY3p4Ral_P4T_GL9MXIVH9GKdTBj9rS8B6ghS3-cOlWcDnlQWhSOsCW3qPzpD1Zzvpc-C4RtYf-DoWR1hjaTUu2o0TwG9b9lUTt0MmcmKXoeirZA2QFDJTmKPEULlkKCQjLP-55ok4PNTQSCpgLpWuDosisVVS07X9cgKb5tk3Bucce4AZ8Bcu_cownefExRmZke7qF9P-amnHiyGFtT8md8Y_a4.WsRP4tdF7JqfuepW0dkPK8v8LdYPYb__41nktxIpsqQ&dib_tag=se&keywords=thermalright+120+cooler&qid=1731773937&sprefix=thermalright+120+cooler,aps,140&sr=8-1&th=1
You'll knock a few degrees off your maximum temperatures with a more capable cooler.
The only time I repaste my CPUs is when I take off the heatsink. Some of them have been running untouched for years.
Possibly, especially if the CPU is hitting the thermal throttling point. I've no idea if the GPU or the CPU in your system is the bottleneck. The fps limit might be due to the GPU, not the CPU.
Only way to tell at the same overclock is to improve the CPU cooling and reduce the temperature by 5 to 10 degrees. If you get improved fps, you'll know the answer.