I ran into this some time in October 2021, and discovered that the keyword "help" (instead of "heal") does the trick:
09:16 Mathias Bynens [638]: help
09:16 Azalea: You are poisoned, my child. Let me soothe your pain.
So NPC Azalea can in fact heal all status conditions. The bug (or at least, unexpected behavior) is that the usual "heal" keyword doesn't work with Azalea, even though it works for all other temple NPCs. Here's an example of me saying "heal" while poisoned:
09:16 Mathias Bynens [638]: heal
09:16 Azalea: You aren't looking that bad. Sorry, I can't help you. But if you are looking for additional protection you should go on the pilgrimage of ashes or get the protection of the twist of fate here.
09:16 Mathias Bynens [638]: help
09:16 Azalea: You are poisoned, my child. Let me soothe your pain.
Compare this to any other temple NPC, e.g. Yberius in Venore:
09:19 Mathias Bynens [638]: hi
09:19 Yberius: Welcome, young Mathias Bynens! If you are heavily wounded or poisoned, I can heal you for free.
09:19 Mathias Bynens [638]: heal
09:19 Yberius: You are cursed. Let me remove the hex.
Note that in Yberius' first message, "heal" is even marked in dark blue, indicating that this is a valid keyword to use. The same is true for most other temple NPCs.
I believe that Azalea used to respond to "heal" correctly until some time in 2020. I reported it as a bug to CipSoft in October 2021 (Ticket#20211011420020).