I look at Bluetooth settings on my PC and it cannot see my Echo Dot listed BUT if I ask what my next appointment is, it correctly reads my calendar?
The first statement as nothing to do with the second... Your dot is on your wifi, your computer has nothing to do with that.
So I'm failing to see any issue here?
If you have spotify premium, your pc is not needed to listen to spotify on the dot, however spotify knows you are, as evidenced on the website. You can turn off your pc and still use spotify on the dot. Or access your calender. Or control any home automation you may have. Or ask Alexa questions etc etc.
If all you want is to control spotify using your computer, a simple bt speaker would suffice. What you bought is way more of a stand-alone system and I'm thinking you don't get that..?