Can't group by field inside facet

Could you explain please how I must use match by pointer inside pipeline?
I have code like from my previouse question, and at once found that not only comparing by date does not work. equalTo also had no effect. I guess that I need move equalTo to date comparing to match stage inside pipeline, but I don’t know what is right syntax must be.

Because for date comparing { match: { createdAt: { $gt: DateObj } } } work fine by analogy I tried with { match: { pointerFieldName: { $eq: pointerObj } } } but without success. May be there are own tricks for that?