Bug in VectorDensityPlot assigning variables

Question

Bug introduced in 12.0 or earlier and fixed in 13.2 or earlier

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I notice that after a call to VectorDensityPlot the variables used are assigned to random real values. This doesn't seem to happen with VectorPlot and I can't find a notice of bug. It's been mentioned in other posts (e.g. Bug in VectorFieldPlot[] with InterpolatingFunction[]?). Is this a know bug? Does it affect all versions (I'm on 11.3)? Is there a suggested Block? Evaluator?

ClearAll["Global`*"]
f[xy_] := {xy[[1]]*xy[[1]] - xy[[1]] - xy[[2]]*xy[[2]], 
  2 xy[[1]] xy[[2]] - xy[[2]] + Pi}

{x, xa, ya}
VectorPlot[f[{xa, ya}] - {xa, ya}, {xa, -2, 3}, {ya, -2, 2}, 
 VectorScale -> Medium, VectorPoints -> Fine]
VectorDensityPlot[f[{xb, yb}] - {xb, yb}, {xb, -2, 3}, {yb, -2, 2}, 
 VectorScale -> Medium, VectorPoints -> Fine]
{x, xa, ya, xb, yb}