I had similar concerns but read that there's no harm. Also have miscarriage history. In fact doc later said that I needed a double dose because my progesterone test levels came back quite low. The pills take a bit of time to get used to and may cause a bit of drowsiness, but after a few days your body will get used to it. Hang in there! We probably only need to take for first trimester until the placenta takes over the hormone production.
My Gynae prescribed me with progesterone pills for my first pregnancy and did not do any blood tests when I was week 4 too. It’s to help sustain early pregnancy and my baby came out well. This is my 2nd pregnancy too and he also gave me progesterone pills. I’m now week 5+.
The dosage usually is quite mild and commonly prescribed as a precaution