7970 is still a good(but power hungry) card.
It is a bit stronger than a GTX1050ti on tom's gpu hierarchy chart.
https://www.tomshardware.com/reviews/gpu-hierarchy,4388.html
Your FX-6300 on the other hand is obsolete with no upgrade available on whatever motherboard you have.
It has a passmark rating of 6384 when all 6 threads are fully utilized but only 1408 as a single thread rating.
Most games depend on fast single thread performance.
Few can use more than 2-3 threads.
To see how many threads YOUR games can usefully use, experiment with removing one or more cores/threads. You can do this in the windows msconfig boot advanced options option.
You will need to reboot for the change to take effect. Set the number of threads to less than you have.
This will tell you how sensitive your games are to the benefits of many threads.
If you see little difference, your game does not need all the threads you have.
You are looking at a modern cpu upgrade which will also require a new motherboard and ddr4 ram.
ryzen is popular if you need many threads.
Intel wins out in the single thread performance category.
For example, even the $65 4 thread G5400 has a passmark rating of 5255/2200.
My guess is that you would be most satisfied with a 6 thread I5-8400 passmark 11745/2334.