My impression is that Emma was very jealous of Harriet, even if the qword jealous is not used -- about not being cold to Harriet, it was only when she wanted to hear from harriet what were her reasons for thinking Mr K returned her affections. After listening to them -- 'the spontaneous burst of Emma's feelings: "Oh God! that I had never seen her!"'(chap 47)

Emma wished she had never seen Harriet! I find that to be a reaction of extreme jealousy. She also wished that --
"Oh! had she never brought Harriet forward! Had she left her where she ought, and where he had told her she ought!" i.e. that she had left her "in the line of life to which she ought to belong,", and "It must be her ardent wish that Harriet might be disappointed;", and "In the meanwhile, she resolved against seeing Harriet. ... She wrote to her, therefore, kindly, but decisively, to beg that she would not, at present, come to Hartfield; acknowledging it to be her conviction, that all farther confidential discussion of one topic had better be avoided;".(chap 48)

Of course, Emma used kind language, she could not be rude or expose her jealousy.

I'm not criticizing Emma for being jealous. It was Mr K's jealousy of Frank that made him reaize he loved Emma, and it was Emma's jealousy of Harriet that made her realize she loved Mr K!