Androgens (i.e. testosterone and DHT) increase sebum (oil) production in skin, progesterone as well but to a lesser degree whereas estrogen DECREASES sebum production. Progesterone helps to counter dry hair/skin and sometimes brittle nails (caused by not enough oil in skin) caused by estrogen AND the loss/reduction in androgen. During pregnancy, progesterone is high and estrogen as well. They balance each other out. Pre-menopausal ciswomen also typicall have more androgen than us, so more oil.
The addition of progesterone has really helped with my skin/hair dryness. My nails are quite strong. I find estrogen taken orally also inhibited androgen production more than when taken non-orally because orally, SHBG is increased by estrogen to a greater extent and it binds (inactivates) androgens very strongly. On oral E, my skin gets WAYYY too dry, even with progesterone. Not so with injections.