I have a few maps of city sidewalks in Geojson format which I need to manually edit to make corrections. However, in the tools that I've tried, geojson.io and QGIS, segments that share an endpoint are not treated as connected but rather as four separate segments. So when I drag a shared endpoint, it becomes multiple separate endpoints as shown below:

Original map:

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After dragging the bottom left point, it separates into four:

enter image description here

I don't want this to happen; instead I need all the segments to remain connected if I drag an endpoint. Is there any existing tool I can use to do this? Or an easy way to program a custom tool?

I realize this may be a limitation of the geojson format itself, since each segment is just represented as a start coordinate and an end coordinate. But what I'm imagining is a tool that can recognize when multiple segments share the same endpoint, so if that point is dragged, the coordinates are automatically changed for all segments that originally had that endpoint.

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