Progesterone is a hormone produced primarily in the ovaries and placenta in the event of pregnancy. To a lesser extent, it is also secreted by the adrenal glands and the liver.
During the menstrual cycle, at the time of ovulation, the follicle that has released the egg becomes the corpus luteum and begins to produce progesterone. This progesterone is responsible for preparing the endometrium for a possible pregnancy.
That said, when we ovulate spontaneously, progesterone is produced by the corpus luteum. Similarly, if a follicular puncture is performed, the punctured follicles will also become corpora lutea and produce progesterone.
The fact that only follicles are obtained, grown or punctured from one ovary does not determine whether the progesterone is higher or lower. The body does not differentiate laterality in this respect. When hormones are produced, they pass into the bloodstream to be able to exercise their function in other organs, whether they come from the right or left ovary, indistinctly.