The correct depth depends on your frost level.
On a patio the idea is that the freezing doesn't matter so much as long as it is on an adequate layer of compacted gravel. I am talking about stone, not stone with fines in it like what we call Non Grade. So if you have your stone deep enough any moisture will be drained away and wont heave the patio. If the ground below it freezes in unison then the entire patio should move as a unit or the movement should be minimal enough not to matter. The idea of dry laying bricks/pavers has many benefits. The pavers are small units and allow for minor movement from freezing. Also if you need to repair a section it can be done without having to tear up the entire patio. If that was concrete you would need to strike control joints every 5' feet to guide where it cracks.......and it will crack. If you had to repair a section it is a major chore and it wont match the existing. Pavers are the way to go.
In general the rule of thumb in the North is to have a 4" gravel base that is well compacted. I prefer 5". If you are in an urban environment the temps may not be as extreme, especially with a large body of water nearby, like the Mississippi River. The larger bodies of water create a microclimate and if you are near it the temperature ranges tend to be less severe. In general your patio should hold up pretty well and if you experience sinking or heaving you can easily relay the bad section in a few hours. Just pick up the pavers and scrape away or add stone dust where needed, tamp and relay the bricks. The patio may never move, especially if you tamped it well.
I have a degree in Landscape Architecture btw. Anyone that ever wants to message me on landscape advice here at ROD can feel free to do so. I have been installing patios and sidewalks since 1992. Most have never moved, but there are always a few with mitigating circumstances that have settled or shifted. In every case it is a water issue that could not be changed.
The patio looks great! The lights are a nice touch.