How to split Edge that have vertices close to the line?

Hello,
I have a problem, sometimes a situation arises where two faces are connected when one of them is split but the other is not (and it is not a Ngon) so that between the two vertices where they are connected there is a long edge that belongs to the full face and two more edges that are connected to the split face.

There is a hole there, only it is long and thin.

Is there a way to split the long edge into two, depending on the position of the vertex that sits on it?
(sometimes there is more than one vertex sitting on it)

For example:
image

If I move the vertex a little, That’s how it’s built:
image

I am looking for an automatic way to solve the problem, a plugin, or Geometry Nodes, sometimes I have a model with a lot of such problems.

First Select All Faces
Then use Menu → Mesh → Cleanup → Fill Holes,
followed by a “DegenerateDissolve”.

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Add an edge loop at the top and then use the “Remove doubles” command.

Thanks, it works! (Will save me a lot of time)
Remarks:
“Fill Holes” with 0 value (so it will fill every hole)
“Degenerate Dissolve” works on one vertex every time (if many vertices are on the edge) so I need to run it repeatedly in such a case.

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