What is the make/model of your psu?
Software will not tell you that.
Neither will software tell the make/model of your case.
If you play fast action games or if you want to use a high res monitor then a stronger GPU is in order.
As a quick test,
Run YOUR games, but lower your resolution and eye candy.
This makes the graphics card loaf a bit.
If your FPS increases, it indicates that your cpu is strong enough to drive a better graphics configuration.
If your FPS stays the same, you are likely more cpu limited.
If a gpu upgrade is in order, here is a handy chart as to the psu wattage required.
http://www.realhardtechx.com/index_archivos/Page362.htm
For games, the single thread performance of your cpu is all important.
Run the cpu-z bench on your I7-6700.
You should get a number like 397:
https://valid.x86.fr/bench/0gt9vb/1
As a good reasonable upgrade, I might buy a I5-12400 with a rating of 702. About $200.
You will want a B660 based motherboard which will sell for $100-$150.
You can reuse your ddr4 ram.
On the 12400, I would not go $20 cheaper with the 12400F that does not include integrated graphics.
Over time you may find integrated graphics useful if you have gpu problems.
Here is a review:
https://www.tomshardware.com/news/intel-core-i5-12400-review
I5-12400 comes with a cpu cooler, but many will upgrade the cooler.
Aftermarket coolers will come with reasonable paste.
Differences in paste are minimal to the casual user.
120gb is too small for a C drive.
As it nears 90% full, it will lose performance and endurance.
Today, I would buy a 1tb 2.5"samsung 970 evo to replace it.
About $90.
There are cheaper ssd devices, but none as good.
You will not notice any difference from a m.2 pcie ssd.
Use the samsung ssd migration app to do the job.
App and manual here:
Download various software related to your product, including Samsung Magician, designed for use with Samsung's memory products, and find related information.
semiconductor.samsung.com
Then, just boot from the 970 on your new motherboard and install the chipset and motherboard drivers.
Many will recommend a clean install. They have a point, but it is YOU that will be doing the work.
I have found that such a simple upgrade with intel processors works well and would try that first.