Don't seal the castings air tight. Castings are crawling with microbes that need oxygen to survive.

Maybe in the "bottom sump tray" put torn up egg carton or other dry bedding material. When it becomes wet use it as bedding in your next feeding tray.

You do not say how you harvested it but to dry your vermicompost if you are using a tray system, put a tray of brand new, dry bedding material such as torn up egg carton right under it (or not) and put this tray on top. Maybe crack the cover a bit so it will dry out. You want to give the worms a place to crawl to safety and time for any eggs to hatch.

The best way to store them is to NOT store them. To use then right away. It is a living substance with wee beasties your allies, do not suffocate them, they want with all their hearts to do serious work for you in your gardening. Please do not kill them by zapping then into an air tight bag. Bad things will then happen to that material. The bad galls will then begin to grow. They will be mean to your plants.

Maybe to store your wet vermicastings pour them from one bucket to another every two weeks to two months. This will put the wet bottom on top and the dry top on the bottom. The good wee beasties can live in the middle with plenty of oxygen.

""I would now like to store the compost/castings that I just harvested""
Are you still talking about the stuff from the sump tray or is this ""mound of castings/compost is quite damp"" from your stackable trays.
From the sump tray, you could strain it with an old T-shirt or something to get rid of the liquid, then I would put that T-shirt plus muck onto several layers of corr. CB or newspaper to absorb more moisture, and fluff it daily to avoid becoming a brick, and remove visible worms you missed earlier.
If you're talking about your harvest from the VC tray, I usually use an old aluminum roasting pan, lined with corr.CB and/or layers of newsprint and spread the damp VC on it. Then the same routine as above. I let them air dry in the carport and it took several days.