I don't know why you want to do it interactively. You can use QGIS expressions to visualize those points that have a nearest neighbour less than 2 km away and than decide in each case what to do. You can use differnt forms of visualization, I show here one that connects points nearer than 2km with a line.
The advantage to use geometry generator: when you move or delete points, the line immediately adapts to the new situation and the lines change accordingly. So you can observe the effects in realtime. When all lines disappeared, than you are sure that you don't have any points closer than 2 km.
Of course, you could also use a simple expression like
buffer ($geometry, 2000) to draw a 2km circle around your points, but than you have to look manually for points within this distance.
The expression below first evaluates if there are any points nearer than 2km and only than draws a line. You could use this expression as well to generate a new field with the field calculator that calculates the distance to the nearest point, using just this part of the expression:
distance ($geometry, collect_geometries (overlay_nearest (@layer, $geometry )))
But I advice to try this: Add an additional symbol layer to your point layer, set it to Geometry generator, Geometry type: line and paste this expression:
) < 2000 ,
You can see from the measure tool on the bottom right (red box) how far is 2 km on my map canvas and you can see that points with a distance less than this are connected with a line: