Solving the problem with the "Indexing data" window while editing

It's caused by snapping. I guess you could disable that.

Upgrading QGIS might be the better option though, I'm quite sure it has been solved in newer versions.

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Update: Even when they turned off snapping, it continued working in the background. The solution was to open "advanced options" in the snapping menu and disable it for all the layers.

It can also be caused by Show Feature Count in the Layers Panel. Uncheck it, if it is checked.

Just to confirm that in QGIS 3.14, this still persists (from a snapping-indexing perspective at least anyways).