On my GPU on every AMD driver I installed and always clean install mine is always set to 0 (100% power limit which is also what's flashed in the bios by Asus)...
I have a Asus Strix RX480 flashed to Strix RX580 OC and use default power limit and it can keep the max clocks all day long (default is set to 1360mhz), the problem of my current settup is only temps, as soon as it hits 80 something Cº sadly the clocks drop, but using +50% power limit doesn't matter on mine a single bit, however -50% would definitely impact the clocks, but my GPU is always flashed with Asus software to 100% power limit and every time I do a clean AMD Radeon driver install even with DDU the default option is always at 100% for me...
But anyway his problem might be wrong power limit set to half like you sad, but it can also be severe CPU thermal throttling since his CPU uses thermal paste between the chip and the copper metal cover above and some people also had crazy FPS drops and would never play a game well and found it was because of the CPU that needed to be delidded... Intel only went back to soldering the IC on the 9th gen like my 2nd gen I7 2600K which is soldered and never have bad temps, some CPU's from 3rd gen and above up to 8gen can be plagued with bad temps, but usually by now its mostly the 3rd, 4th and maybe 5th gen that will have more problems depending on their use because they are older and if they were used a lot the thermal paste by now is probably not doing much...
And I have seen quite a lot of cases with Intel CPU's which were killing all the gaming performance, it was a very stupid move for intel moving from soldering on the 2nd gen to crap thermal paste above up to the 9th gen where they finally decided to fix so many years later when they screwed it up on purpose...
ps: And if the CPU causes huge bottlenecks it will indeed make the same effect where the GPU will never be able to keep 100% used all the time if the FPS are being capped by the CPU. Anyway both RX580 and that old CPU are both a big bottleneck for modern gaming 
. I'm still much better with my older 2nd gen I7 2600K, but it's OC to 4.9ghz and basically it's giving me close to a 7700K in single thread performance and multithread is similar to the 4th gen I7 K all at stock clocks, but I still get both CPU and GPU bottleneck on like Post Scriptum which is very demanding, basically with no one playing is mostly GPU bottleneck with the RX580 being weak for it and with too many players when there's too many action going on the FPS also drops in a flash and come back up as soon as it ends, but other more optimised games like crap gears5, BFV and others run perfectly fine for me.
It doesnt matter matter if you put new thermal paste or even liquid metal, I'm talking is the thermal paste hidden inside the chip between the die and the copper plate where you then put whatever thermal paste above it, but the problem is what's happening under it...
In most cases on an actual still good thermal paste Intel CPU just delidding it some times have a 20Cº drop right away when using liquid metal instead of thermal paste directly on the die. And if the thermal paste is bad a lot of people run into the same issues as you and have huge lag\poor performance on basically almost all games...
Have you really kept checking temps on the CPU while playing and it's clocks? if the CPU is not always at full turbo and is thermal throttling it might need to be delidded...
The better the GPU you put on your PC and the lower performance is the CPU, the more CPU usage and power will use and the less GPU will use... with your old CPU for example if you had a RTX2080TI as an example the GPU would probably not even be able to pass 20% usage in a lot of games unless at 4K and the CPU would be running probably always at 100%...
Since you upgraded the GPU for something much more powerful, unless you cap FPS it will surely push the CPU much more than before with the older GTX760 so Keep track of the CPU clocks\temps while playing a game to see if that isn't the problem as like I said many, many people have problems with those Intel CPU's that are using thermal paste instead of solder from the die to the IC and require delidding which is easy to do and very inexpensive...
This is an example of the I5 4670K for you to see what I'm talking:
To resume what I'm saying is the older GTX760 being so slow for current games it might not have been pushing the CPU any harder and just having huge GPU bottleneck instead and now with the RX580 it will surely push much more from the same CPU which will put out more wattage and more stress in the same CPU which leads to more heat and if the thermal paste is bad which is already a very old CPU you might actually be having thermal throttle on the CPU.
So like I said open one CPU demanding game that you have which now the RX580 should be able to make that CPU to push higher FPS and therefore push more from the CPU and keep recording the clocks\temps on both the CPU and GPU to try see if dried thermal paste inside the CPU isnt the problem, if the CPU is kept at max turbo all the time and you still have bad performance, then it must be other problem...
Also for faster CPU testing you can simply use 1 of many apps to do a CPU burn-in full 100% test which pushes it to max on all cores and leave it for a while and check the thermal throttling conditions\temps...
I have is the Strix RX480 8GB flashed to Strix RX580 8GB OC, would never go with the crappy 4GB model...
But anyway the GTX770 is already a big step up from the 760 for back then even though nowadays none of them matter anymore as they are all weak even RX580 is getting quite weak for some games ...
And next year will be the release of next gen consoles with Ray-tracing capabilities, it will cripple RX500 series performance even more with games pushing more visuals since the devs know consoles have more juice on them so the PC gaming overall will also start to forget current low end GPU's the more time it passes which is the normal evolution as we all now...
But sadly I don't see any atual good priced gaming GPU that would be worth for me to buy currently... I'm totally going to wait for next gen console release fever to go on and then maybe finally make a new build of a desktop or even wait a little longer for DDR5, no idea since here it's years of savings and I don't want to buy something that will get very outdated very fast... DDR5 will be another big major change and currently AMD doesnt even give any kind of Ray tracing on even a 500€ GPU which next year consoles will have so I'm still gonna hold my horses and don't care about it...
And I also have a kinda cheap 4K samsung TV since 2016 but never had the chance to play in 4K as at this rate of hardware prices keep increasing with low performance improvements, 4K above 60 FPS ultra on all upcoming games for like 2 or 3 years, I might even die before actually having an actual ~350€ GPU that could do it while 4K TV's are like around 200€ the cheapest crapiest ones here. But I tested at least Star Wars Battlefront 1 and Far Cry Primal at 4K ultra settings on my TV with the RX580 and jeez what an amazing visuals even at 1 meter it was crazy detailed, gratefully those games actually run kinda good at 2K without AA, but at true 4K the colors and everything looked much more incredible, from a distance sure 2K vs 4K wasnt much big, but the color difference is HUGE at 4K, but sadly nowadays even for 1080P on most games I have to drop a few settings and my favourite current game Post Scriptum both RX580 and my CPU are too weak, I have to use mostly medium settings, no AA, no distance shadows, not even ambient occlusion and only textures and effects on high, the game looks kinda bad with this settings and still have crazy FPS drops, but sure it's a very badly optimised game that require good hardware like at least something like a I7 7700K with a GTX1070 and even with that I have seen many people complaining bad 1080P performance ...
