Generation and Preservation of Options to Dataset in Version 12.1

Seth J. Chandler
Version 12.1 contains many new formatting options for Dataset.
I have a dataset. I want it Yellow.
In[]:=
dataset=Dataset[{{1,0},{0,1},{1,1},{0,0},{0,1},{1,0},{1,1},{0,1},{0,1},{1,0},{0,0}},BackgroundYellow]
Out[]=
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
Now I want to run a Query on it.
In[]:=
q=QueryGroupBy[#[[1]]&]/*KeySort,(GroupBy[#[[2]]&])/*KeySort,
Length[#]
11.
&[dataset]
Out[]=
0
0
0.181818
1
0.363636
1
0
0.272727
1
0.181818
Notice that the “Yellow” option is not inherited. That is perhaps sensible default behavior, but what if I want to preserve the options. How do I do it?
Moreover, what if I want the elements of the derived Dataset to be kept internally at their full length but presented so that they are rounded to two decimal places. I could do the following icky thing in which I go from the Dataset to Normal form and then back to Dataset.
In[]:=
q2=Dataset[Normal@q,ItemDisplayFunction(Round[#,0.01]&)]
Out[]=
0
0
0.18
1
0.36
1
0
0.27
1
0.18
Annotate doesn' t work :
In[]:=
Annotate[q,ItemDisplayFunction(Round[#,0.01]&)]
Annotate
:-- Message text not found -- (​Dataset[2]​)
Out[]=
Annotate
0
0
0.181818
1
0.363636
1
0
0.272727
1
0.181818
,ItemDisplayFunction(Round[#1,0.01]&)
Nor does SetOptions :
In[]:=
SetOptions[q,ItemDisplayFunction(Round[#,0.01]&)]
SetOptions
:Argument Dataset[2] is not a symbol or a stream.
Out[]=
SetOptions
0
0
0.181818
1
0.363636
1
0
0.272727
1
0.181818
,ItemDisplayFunction(Round[#1,0.01]&)
And again, notice that Query does not let one cause inheritance of the options . The rounding is gone.
In[]:=
Query[All,All,#/2&][q2]
Out[]=
0
0
0.0909091
1
0.181818
1
0
0.136364
1
0.0909091
Moreover, none of this is the fault of Query. Here’s the same code as I tried initially but performed without use of Query.
In[]:=
GroupBy[#1〚1〛&]/*MapGroupBy[#1〚2〛&]/*Map
Length[#1]
11.`
&/*KeySort/*KeySort[dataset]
Out[]=
0
0
0.181818
1
0.363636
1
0
0.272727
1
0.181818
Is there a workaround. Do we need an Inheritance option for Dataset or Query?