You are seeing the default edge-breaking actions in SketchUp.
New geometry will automatically intersect with any geometry that already exists in the same context.
This is often the preferred outcome.
BUT if you want the circle NOT to intersect with existing geometry, then first make a group [or component] of the existing rectangle etc, then draw over that to make the circle, which will no longer be in the rectangle’s context and so it will not interact with it.
Later on if you wish to change the rectangle you simply edit the group [or component] and when working inside its context intersections will be reestablished…
Groups and Components are used to ‘separate geometry’, otherwise geometry will interact [usually by intersection or merging].
Do not think to use Layers to separate geometry.
Layers are used simply to control visibility.
Draw all geometry on Layer0 and assign other Layers to the Groups/Instances you make containing that geometry.
That way the interactions are prevented and the visibility is properly controlled, without unpleasant surprises down the line…
This splitting of edges should not move any vertices.
BUT if your geometry is very tiny, then the 1/1000" tolerance might be reached though ?
Scale up and see what happens…
Alternatively, you can switch off the auto-intersect by using this code-snippet in the Ruby Console, applies during that session.
To reinstate the default use:
However, I recommend that you learn to use Groups/Components and get used to how SketchUp makes and interacts its geometry…