Alas, no. There is no indication of what can be stunned, just interrupted. As anyone who's done a lot of deep dungeon solo content will know, to our pain. ("Ack, the mimic's casting Deathtrap, I'll just stun and... CRAP. Guess that's back to floor 1.") Eventually, you commit to memory which mobs are vulnerable to stun and which are not...
The theory, as I understand it, is that anything with an interruptible cast bar is, functionally, something with the equivalent of a D&D spell's "Verbal" component -- e.g., something which requires you to speak an incantation aloud. Hence why interrupting them will end the cast, and why 'Silence' can prevent spellcasting entirely... and the justification for the cast bar blinking, as you can hear the enemy/creature/whatever performing the incantation.
To be fair, with very few exceptions -- the sludge from the worm in Cutter's Cry, the Doom-by-a-different-name debuff from the first boss in the Dead Ends, etc. -- the majority of debuffs inflicted in dungeons are so short in duration that they're almost not worth using Esuna on. If you get a 6 second poison debuff, chances are by the time I've finished the GCD I already had going, seen the debuff, selected you, and then cast Esuna, the debuff's already about to vanish anyway.
Generally speaking, if someone has a short poison debuff, it's more efficient to heal them through it than cleanse it. (A long poison debuff is obviously more worth cleansing.)
This is doubly true if it's, like, an 8s paralysis debuff inflicted on the party. Murphy's Law of "screw you" means that my first cast of Esuna (on myself) will be interrupted by said paralysis. My second cast will almost assuredly cleanse my paralysis, but by that point we're probably around 5s into the 8s debuff as it is; with only 3s left, it's almost not worth cleansing anyone else.
Now, to be fair, the exceptions to the "it's not usually worth using Esuna on dungeon debuffs" rule are generally speaking ones where you really want to use Esuna. (Such as the aforementioned Doom-by-a-different-name.)
And I absolutely 100% agree the game could do far better at teaching folks that the white bar atop a debuff icon means "you can cleanse this with Esuna", since I do not believe the game makes mention of that anywhere.