Is it intended that CoefficientRules permutes exponent vectors when given a monomial order?

Question

Bug introduced in 13.0 or earlier. Fixed in 13.2.0 or earlier.

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I noticed an odd behavior in CoefficientRules when you give it a monomial order:

In[1]:= r = CoefficientRules[t^2 + 3 u, {u, t}, "NegativeDegreeLexicographic"]
Out[1]= {{0, 1} -> 3, {2, 0} -> 1}

In[2]:= FromCoefficientRules[r, {u, t}]
Out[2]= 3 t + u^2

Without "NegativeDegreeLexicographic", then the exponent vectors respect the {u, t} order and FromCoefficientRules results in the expected t^2 + 3 u. Since FromCoefficientRules doesn't take a monomial ordering as an argument, this has the appearance of a bug, but I wanted to check that I wasn't missing something about CoefficientRules before reaching that conclusion.

Maybe a clearer example is this:

In[1]:= r = CoefficientRules[a + 2 b + 3 c + 4 d, {a, b, c, d},
  "NegativeDegreeLexicographic"]
Out[1]= {{0, 0, 0, 1} -> 1, {0, 0, 1, 0} -> 2, {0, 1, 0, 0} -> 
  3, {1, 0, 0, 0} -> 4}

In[2]:= FromCoefficientRules[r, {a, b, c, d}]
Out[2]= 4 a + 3 b + 2 c + d

It seems to be reversing the variables completely, maybe a consequence to how "NegativeDegreeLexicographic" might be implemented.

Answer 1

r = CoefficientRules[t^2 + 3 u, {u, t}, "NegativeDegreeLexicographic"]

gives

{{1, 0} -> 3, {0, 2} -> 1}

and

FromCoefficientRules[r, {u, t}]

returns

t^2 + 3 u

Likewise for the other example from the OP.

A screenshot for clarity and completeness