What’s the best use of time in the dragon trial? In your opinions?
It depends on your build and interest.
Cavern unlock some runes if you're a Lunargoth or you can get a Writ of Favour of the Northern Army,for now not that useful.
Leona and Fang quest are also opportunity for more romance.
Leona might give you a sword if you didn't take one during the Heist and Fang a sauna that will increase retainer strength.
Dessy has a very important romance event
Graveyard,Steel Thread,Cherry blossoms are all events that give rewards and boost
Wight is very cool imo because it breaks ML and increase Wind/Akakiru Mastery.
Guiren also give Earth/Water Mastery if you're not enemies or a powerful Soul Treasure.
So usually I go 2-3 companion quest
And 3 rewards event when they're at 1 hour.