I would like to raise the handle bar of this bike so I can ride in more of an upright position. I tried searching for methods to accomplish this, but I'm not sure what I found were applicable to this bike. Do I just use an allen wrench to loosen the top nut in the picture below? The handle bar wouldn't budge though. Also does this fork look like it can be extended? Thanks in advance.
You can't, really. It may be possible to get a few millimetres by adding another shim/spacer under the stem, but there's got to be a lot of steerer tube inside the stem too.
Your options are to extend the threadless steerer using an aptly named "threadless steerer extension" which look like this:
from Are stem height extenders safe to use?
But simply raising the bars will move their position relative to the seat - they'll go up but will effectively be CLOSER to your saddle... that is the position won't move in an arc. So your back will end up becoming more vertical.
You can get adjustable stems, but they're a little heavier because of the additional metal. These are often used to dial in a fit and then you buy a fixed stem with the same effective angle.
Your third option is to replace the handlebars with something a little more "raised" For example here are three different bars in the same brand, with various levels of "rise" but the same "upsweep"
Here's the difference:
Your best option here is to imagine where on the bike you want the bars to be, and then figure out how to get them there. Smaller movements will be better than bigger movements, so sit over your bike and visualise. Good luck!