How deep should the soil be in a raised planter??

Depends on what you want to grow? 6 to 12 inches. See if these help.

https://www.almanac.com/content/how-build-raised-garden-bed

https://youtu.be/Bgiemm99Va4

https://youtu.be/k9nL8YLpjEk

https://www.youtube.com/watch?v=S6ZNvkheLcU

6 inches for most veg crops, tomatoe roots need 12 inches. you can google "what size containers for vegtables" and get a decent list.

My raised garden is approx 16 inches high. The soil inside comes up to approx 12 inches high. Leave yourself some room to allow moving soil around to plant. Also you may want to add fertilizer, sand, or more soil after everything is planted. My raised bed was built last year. My sons built it for me. They laid down weed fabric before they put my soil mixture in. We used one-third soil, one-third manure, and one-third sand. The sand is for water retention. I hope this info helps you. Good luck with your new garden.

On average 10 inches

I’ve read about 2/3 of the dept of your planter box

It all depends on what you are planting, google the depth needed for what you have in mind. Some crops are shallow and you don't need much soil, others like tomatoes need depth for the root structure.

I have an elevated garden. It is 4’ wide x 4’ long x 6” deep. It works fine for me.