Ivy etched armor available, but Stormhealers is not? Are they not both the same type of newbie armor quest? Is there any armor quest available for Cleric like Ivy Etched on Agnarr?
Ivy etched is the class armor you get in your 20s-30s. Stormhealers is newbie armor that was added in (I believe) LoY. That won't be around for a long time (if ever? I forget if LoY is coming out on Agnarr). This is what you are looking for in Cleric armor: https://wiki.project1999.com/Armor_of_the_Priest_Quests
FWIW: I looked at one of my original characters on a live server I ran decades ago & put on the shelf , a Ranger. They were ~level 65 and still wearing banded pieces. It's certainly better to have good equipment and it's better to have balance between classes. It is only necessary to have things good'nuff to progress. One of the advantages of TLP is the good stuff is coming soon.
Newbie armor was added later. Ivy Etched is part of the armor sets you quest for in then20s and 30s. Armor of Ro for Paladins for example is also in this vein. So to answer your question OP, no newbie armor sets are in game on Agnarr.
I think Halfling Rogue Armor is actually in. Possibly High Elf Paladin and Cleric. Qeynos Bard Weapon as well.
I haven't seen anyone with the actual "newbie armor" the OP seems to be referencing, as they'd be so incredibly OP that nothing would compare until planar armor, so EVERY Pally High Elf for example would for sure be wearing them. Items for the newbie armor quests were still in at Agnarr launch (just couldn't turn them in anywhere). I THINK patch notes indicated they fixed that. Also worth noting that SOME early armors are in era that are quested and aren't actually the "newbie armor" popularly referenced. I'd be very surprised if Daybreak has left some of these armors in still despite many previous TLP servers for practice. But, you never know I suppose.
It must be available on Phinnigel since my newbie druid found there strange items such as "arc ogre head" in crushbone and around. druid guild master also gave me a container .... I m very sure that no such lore Ogre head existed in classic, we had armor quest to get leather armor and patchwork one .... and yeap we had totemic/lambent and other class armor from the mid 20 onto the 30 ....
Phinigel has PoP and LoY unlocked, which is when the newbie armor quests unlock. Agnarr will get the newbie quests once they open too. For now, you can only do the classic Sol Ro type quests such as Lambent, Crafted, Ivy Etched, Darkforge, etc.