I added some custom CSS values that have higher values than the modal z-index, but nothing changes. Why doesn't this work?

Custom CSS in the v2 picker is loaded inside of the dialog iframe and doesn't affect the dialog wrapper.

To change the modal z-index, place your style on the website where the modal is loaded and include an !important statement in order to override the default styles.

For Example:
.fp__overlay {
	z-index: 10000 !important;
}