Which build should Annie follow when she wants credible kill threat without dying before her combo?

The most reliable build remains a burst AP base that keeps enough safety to enter cleanly once. Annie does not need to live long after the combo if the useful target dies immediately, but she still must buy enough margin not to be cut down before dropping Tibbers and emptying her rotation.

When should Annie's build be adapted?

You should adapt as soon as the standard instant-deletion plan is no longer honest: poke that exhausts Annie before entry, frontline that absorbs the whole first cycle, or assassins that kill her before the decisive animation. From that point, slightly less pure burst but much more right to enter often creates far more real value.

Which enchant should Annie choose to preserve entry threat without sacrificing all burst?

Protobelt generally remains the most coherent enchant because it solves Annie's most expensive question: actually reaching the distance where stun becomes lethal. It is only surpassed when the game first demands a more defensive answer to buy that same angle without dying before exploiting it.

Annie Wild Rift Best Build Guide (Patch 7.1h)

Annie does not play extended fights but instant executions. Her build must maximize the value of her single impact window: the stun. Each item either ensures access to the target or guarantees the combo kills before retaliation.