Try to considering Zeke's Harbinger as your main support item. As there is no Gold income from Zeke, buying Spellthief's Edge is gold efficient and mainly develop core items. Zeke needs to finish its (2,250 gold) to get the passive (Upon reaching 100 charges, you can activate the passive to grant the both of you and bind ally 20% increased AP and 50% critical strike chance for 8 seconds.)

You have no leisure time to develop Spellthief's Edge to Frost Queen's Claim. Just go on Zeke (but sightstone first).

It provide enough mana, armor and AP. with health from sight stone, it is balance for bot lane.

!!! (DO NOT upgrade to Frostfang)!!!
There is NO mana issue (if you use mana right) because you have 200-250 Mana Sapphire Crystal/Zeke.
for LV10 Zyra, 25% addtional mana regeneration is around 36 mana per min. (stay 7 mins to regenerate). So, upgrade to Frostfang is meaningless.

Noted that you will sell Spellthief's Edge when you want to get rylai.

Pros

+ High damage + High CC + Good protection to ADC and team + Good AP substitute if mid-lane go AD + Fun support (like a carry more than a support)

Cons

+ Your ADC need to know When/how to use Zeke’s Harbinger and not to waste that 8 sec + need to have better mana control + Need good positioning and let you alive

Try to considering Zeke's Harbinger as your main support item. As there is no Gold income from Zeke, buying Spellthief's Edge is gold efficient and not to occupy only one item space. You may upgrade it to Forstfang(I am still testing upgrade or not for mana regeneration), $500 to upgrade it is not that efficient even that it make some addition golds. But you found that you will finally sell it when you try to buy Rylai without item space. !!! (DO NOT upgrade to Frostfang) !!!. There is NO mana issue because you have 250 Mana Sapphire Crystal/Zeke. for LV10 Zyra, 25% addtional mana regeneration is around 36 mana per min. (stay 7 mins to regenerate). So, upgrade to Frostfang is meaningless.

First item for every support. Support is responsible to ward river to protect dragon/ mid/ bot lane. Buying ward is too expensive (30mins game need 23 wards x $75 = 1,725),therefore just buy the sight stone as soon as possible

New support item, you will found that it finish when the lane phase nearly end. Therefore, it is not mainly used in bot lane. But it is really useful and the highest win rate item in this version. Just buy it after sight stone instead of other items. ***When you finish it, you have to follow the bind partner (mainly ADC), you have to follow with boots, check your ADC’s boots upgraded or not.

Of course, AP carry needs Magic penetration. Also, You have to follow the bind partner (mainly ADC) due to item Zeke’s requirement

Support is always behind golds to others. Passive of Liandry's Torment is a trick (Max. 12% current enemy health damage). It don’t need high ability power(need many golds) and you can get high damage to tanks. (Zyra is backline of the team, and you face tank in normal case teamfight)

Just do this, this item benefit more than penetration. Your all skills set benefits and Liandry's Torment need this item.

Save yourself and win the game. Sometimes you want to place a good Ult and let yourself dangerous. This item can save yourself after placing good Ult.

If you don’t think zhonya's hourglass is needed and you confident not to die easy, Void Staff is better choice