coefficients not returning coefficients in the coefficient ring

Nobody has claimed this yet.

I recently got reminded of an issue that's been bothering me for years:
why does `coefficients` return the coefficients of a polynomial not as elements of the coefficient ring, but rather of the ring itself? this makes no sense to me. Maybe at some point `promote` didn't work well and so it was more convenient this way?
Example borrowed from the doc:
```
i1 : R=QQ[a,b,c,d,e,f]

o1 = R

o1 : PolynomialRing

i2 : S=R[x,y]

o2 = S

o2 : PolynomialRing

i3 : F=a*x^2+b*x*y+c*y^2

2 2
o3 = a*x + b*x*y + c*y

o3 : S

i4 : (M,C)=coefficients F

o4 = (| x2 xy y2 |, {2, 0} | a |)
{2, 0} | b |
{2, 0} | c |

o4 : Sequence

i5 : C -- should be in R but is instead in S, forcing pointless "lift"

o5 = {2, 0} | a |
{2, 0} | b |
{2, 0} | c |

3 1
o5 : Matrix S <-- S
```
tangentially related: #2490

Start with the `coefficients` entry point and reproduce the Macaulay2 example in the issue; also review the tangential issue #2490. Done means the returned coefficient matrix contains elements of the coefficient ring R rather than the larger polynomial ring S, without requiring the reported pointless lift.

Written by the indexing model from the issue text.