Yeah, so it leads me to conclude that it might just be
Megalomaniak Mind you it could be as simple as since your project isn't very demanding yet every little thing can cause a relative spike. Once you have more demanding things going on both graphically and with regards to physics the things that are currently noticeable as significant spikes might become just comparatively small noise.
Or it could be something in the core of godot that will get fixed in the upcoming releases in which case you have nothing to do until then but just keep working on your project and updating it to newer point releases of the engine until one of them fixes this. But again, it could also be that as your project complexity grows it over takes this and the current stutter you perceive will disappear on it's own as just minuscule background noise.
This is why the age old adage is not to optimize early. Seriously read the link, it actually refutes the notion that you shouldn't be concerned with optimization but the point still holds, you also shouldn't get bogged down with trying to optimize something that turns out not to be a real issue at all in the end.
If you are really still desperate to test something out though, you can try adding a script to every node in the scene and in the _ready(): set the nodes processing to false. Mind you that would just confirm my background noise theory. By default every node processes, just a node without a script processes nothing.
The cost is really tiny, but as I said, if you don't yet have much going on in your project it might seem more significant that it really is.