Hello @mamamimi and welcome to Mayo Clinic Connect. Your experiences tell me you are quite in tune with your body. There is a chance, according to this artcile, that your HRT may not suppress ovulation, therefore, causing a spike in progesterone levels which could account for your nipple soreness.
- Incidence of ovulation in perimenopausal women before and during hormone replacement therapy:
https://pubmed.ncbi.nlm.nih.gov/8605779/#:~:text=These%20findings%20reveal%20that%20HRT,in%20perimenopausal%20women%20using%20HRT.
From the article:
These findings reveal that HRT with the higher dose Prempak-C does not suppress ovulation and that an elevated FSH does not always indicate the absence of ovulation. They also show that neither age nor regularity of menstrual cycles can be used to predict the need for contraception in perimenopausal women using HRT.

Did your doctor mention this being something you may experience?