Right. This means it would always appear when you first open Brave. So opened until you close it.
Right, which means it won’t open unless you hit the button to open it.
Well, if it was set to Always like you mentioned, then it means it would open by default. That’s how. But if it’s set to Never and you open a new window, it shouldn’t open. The only way it would do so is if you hit the button for it, which is next to Wallet and all. Not sure if yours will look the same as mine as I have Media Router enabled as well, which allows me to cast my screen to Chromecast and all. But the Sidebar button, which you have enabled, should look like:
You’ll notice on mine, there are 4 buttons there. The one I circled and have arrows pointing to is the Sidebar button. If you click it, it opens/closes the sidebar. It works even if you have it set to Never in settings.
If you’re not familiar with the others, on left is button for Extensions. It only appears if you have extensions added to Brave. Then to the right of that is the Cast button, which lets you cast to another device. Then to the right there is Sidebar. Then to right of that is Brave Wallet. To the right of that is VPN. To the right of that is Hamburger Menu 
which is how you access Brave’s settings, History, etc.
Saying all that, let’s rewind. If your setting was for Always, then it would have opened your Sidebar by default. If you had changed it to Never, it would have remained open until you closed everything OR until you hit the Sidebar button to close it.
If you currently have settings to Never and you disable that button, (you see where my screenshot earlier has the toggle off, right?), then Sidebar should have no way to open. To my knowledge, there’s no keyboard shortcut to open it.
Guess short answer on how it opened is either (1) You hit the button to open it -or- (2) It’s because Always was in your settings, so it opened as it was told to.