I lost star seller status this month because I had 4 orders from same person and shipped them together under same tracking number. I wasn’t aware I had to put the number on every custom order listing because it gave a drop down list with shipped together with another order, as an option. That is literally the only thing that marked me down. Everything shipped out on time or early. All other categories were at 100%. Is there anything I can do or is it even worth fighting for?
I think all you can do is wait.
Has 3 days passed since you sent the Orders? You have 3 days to add / update Tracking after you complete an Order. If you can add the Tracking now, it will not correct the statistics for the Badge/s awarded for April, but it will correct the statistics for the May SSP data.
Otherwise, there is nothing worth "fighting for" as Etsy has been steadfast in refusing to manually change SSP data due to Seller error / oversight.
Nothing you can do but learn for the future. Not worth fighting for.