My case is a bit different than most since my NVC expedite was approved and the file went to Frankfurt without being reviewed by the NVC. At least I think that is unusual.
I emailed the expedite request to the NVC email address on 3/31 and submitted by documents on 4/4. They approved the expedite 5/26 and I requested permission to set an appointment shortly thereafter. I logged in om 6/9/2022 and these dates are available.
June 27, 28, 29
July 1,5,6,7,8,11,12,14,15,18,19,20,21,25,26,28,29
They released the June dates around the end of May if I recall correctly.
I would suggest you schedule your medical if you have not already done so. Vilnius was where I went and I did a post today about the experience in the Ukraine forum. Highly recommended.
Good luck