A transcription factor, by definition, is a: molecule that controls the activity of a gene by determining whether the gene’s DNA (deoxyribonucleic acid) is transcribed into RNA (ribonucleic acid).
source: https://www.britannica.com/science/transcription-factor
So to go by definition, β-catenin should count as one, since it (through TCF/LEF) controls the expression of Wnt target genes. However, I've rarely ever see it mentioned as such. Most studies I've come across call it a coactivator of transcription factors, so I'm not sure whether my terminology is acceptable. I mean, can I call it a transcription factor in my thesis/publication?
(P.S. here are 2 examples I found where they do deem it as one: