Kozouki

The GPUs between brands are the same.
But remember that the 1660 Super is better than the 1660.

If you search the review sites there are differences in performance that may arise from improved component quality, but it's rare that board partners offer anythibg significant over their competitors.  However, high quality binned GPUs vary from base-level boards in their ability to overclock, which is why the completely unlocked EVGA 3090 Kingpin is several hundred dollars more than other 3090 options.
 
Top end cards are only worth it for extreme overclockers, or gamers with high performance custom water cooling loops that plan to run a moderately-high overclock for daily use.

Also some brands have RGB integration with other components which, if your into that sort of thing, might be of value. When I shop between brands I also tend to look at customer service records and warranty provisions just in case

They should all have the same performance, the chip should be the same in all of them, the only thing different in the brands are how they cool it. So at most you might get high temps if you pick 1 brand over the other.

the performance will vary little to nothing, due to the boost clocks the card will apply automatically (and the fact that you can get a better/worse chip just by chance).
the differences are mainly in the:
- Cooler (size, noise, looks)
- Connections (HDMI/Displayport config may vary)
- Support (who do you contact when there is a problem with your card)

"component" is a synonym for "part", as in part of a whole.
Anything you use to construct a "computer" is a part of said computer, thus a computer component.
 
This includes parts such as a CPU, videocard, case, storage devices (HDD, SSD, etc.), Etc. Etc.
"Computer component" can also be an item not everyone uses in their PC, such as fan/RGB controllers and those types of optional components.
 
Reason I put computer in quotes above, is because some people may not think of a desktop PC as consisting of parts, but think of a computer in a whole sense.
These are generally the people who don't know too much about PC's, or those that won't have the time to work with individual parts of the PC .
 
Someone like this might not say "my video card is broken, let's replace that", but would rather replace the entire desktop. This is because in their mind, a computer is a full singular device and doesn't hold value as individual parts.
People like this, might classify a whole setup (including the desktop, monitor, keyboard, mouse, etc.) As a computer and their concept of a computer component/part would then be different as to what you or I think off when saying computer component.
 
So in short, a component is a piece of one whole, it just depends on how far you want to specify something as a part.

Components are parts

Components, as I understand it, is the CPU, MOBO PSU etc.

I would say the CPU would have an impact on modern game frame rates yes, you would likely not be able to make full use of the capability if the GPU where it is being taxed heavily.
 
You may wish to spend less on a cheaper GPU but that may result in even lower frame rates.
 
I also agree the 5600XT is a good choice to maximise GPU utilisation without risking lower frame rates of an older GPU.

good value is more important, you would run into some bottleneck issues in modern AAA titles but for rendering and any slightly older titles the 1660 super will do well for you