I don’t think Tink could be the Godmother as Snow/s kingdom never had one for hers so why would Regina get one. Also, remember with Kathryn in SB, she said that she never had a friend.
That’s true but she told Maleficent that she was her only friend. So she’s not exactly telling Katherine the truth. Mal was her friend as the EQ, Katheryn was her friend as Regina Mills, Mayor of SB. So it makes sense that she would have at least one friends Regina, young innocent soon-to-be-queen
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"He was a lot of things to me" "The only conclusion was love"