It sounds like you are on sequential HRT, and can therefore expect a plumper, juicer endometrium than the postmenopausal cut off of 4mm, which was derived from untreated women with shriveled, atrophic everything!
There is a lot of inappropriate investigation of women in this setting due to outdated guidelines and lack of education of clinicians.
I would not take the progestin with the hope that it will directly and immediately improve your psychological state - it is indicated only for endometrial control.
However taking it over the long term should give you peace of mind in as far as preventing endometrial hyperplasia.
Additionally dydrogesterone (nalvee) is one of the kindest progestins, free from some of the negative effects on mood that others such as micronised progesterone or norethisterone can induce.