Hello!
Yes, that is intentional, the other side can be unlocked from the Earth trial, this is a path that allows quick access between trials once both sides are unlocked.
The boss fight at the Essence caverns drops a broken key that can not be used to open the locked gate. If you check your mixing station, In any purchased house, you can repair it.
Hope this helps!
If you have any other issues, or they persist, let me know.