Please take the time to read fully first. Don't start doing things as you read.
Especially read the last part and see if that's the issue before going through and doing other things.
you don't cap your framerate with V-Sync or anything like that. if there is an option in game settings to limit framerate to a specific amount, limit it to any amount that is below the refresh rate of the monitor.
If there is no option to limit FPS, can always crank up the graphic settings until your frame rate stays below the limit.
Also, nobody ever said G-Sync would fix stuttering. You asked if G-Sync is worth it and if it would remove the screen tearing and yes, G-Sync will do that, but stuttering is a completely different thing.
Stuttering can be a GPU issue, but GPU isn't the only thing that can cause stuttering. CPU, RAM, drivers, and storage can all cause stuttering.
To be able to use G-Sync, you need to enable it for both full screen and windowed applications that way, and it's always best to run your games in full scree and not borderless.
Disabling full screen optimization on games games can also help.
Disabling all gamebar/dvr related services in Windows settings is also a must.
make sure you have DirectX properly installed and updated.
Best way to do that is to download and install the SDK
https://www.microsoft.com/en-us/download/details.aspx?id=6812
Make sure windows is fully updated.
Make sure you have the latest drivers installed for your hardware and hardware controllers.
But again, this is for stuttering.
And according to your latest post, you are also getting screen tearing when G-Sync is enabled?
Also, your post is a little confusing.
You asked specifically and I shall qoute:
And what you just said right there is the same as saying you want to play at 60fps, but while playing at 144-165fps?
Frame rate, and refresh rate are tied together.
If you play at 60fps, then the refresh rate of the monitor at that moment is 60Hz because 60Hz means that the monitor is refreshing 60 times per second, and when you play a game at 60fps, (and synchronize using whatever sync method available), then the monitor will be able to display each individual frame per second because they match.
Now, if what you are saying is you enabled V-Sync and limited the frame rate in game to 60fps/60Hz, and you are saying that nvidia control panel is only letting you select a 60Hz option for your monitor at that moment, then that is because you enabled V-Sync.
If what you are saying is that you didn't enable V-Sync but you set the in game limiter to 60fps/60Hz, and nvidia control panel is only letting you select 60Hz, then we can troubleshoot that.
But most importantly, if what you are saying is that you can't enable G-Sync or you are saying that nvidia control panel doesn't let you select anything but 60Hz no matter what, or both, then I will say you need to make sure you are connecting to the monitor using a Display Port cable.
HDMI will not cut it.