The Most Simplistic Theory.

>Cortana is Rampant (logic plague or not)
>Chief doesn’t want to destroy Cortana but rather cure her of rampancy.
>Halsey tells him to go to installation 07. To find Mendicant Bias’s deactivated core.
>Mendicant Bias was put under a ‘process’ to ‘correct’ it’s rampancy. (Halo Primordium p.356)
>Chief is looking to discover this ‘process’ in order to ‘correct’ Cortana’s rampancy.

That’s the baseline, and then everything can be revolved around this main idea behind the plot. Simple, introduces a character not physically seen before in the game (heard about) but not seen) yet easy enough to explain to casual fans through the form of cinematics while still leaving an appeal to the lore artists of Halo.

Thoughts?

The “correction” process was the separation of him into parts that were scattered across Forerunner-controlled space. However, this was undone after the Flood found his parts and reassembled him. After that, he had his final defeat at the hands of Offensive Bias, and then he was imprisoned beneath the Ark as punishment. The only piece of him we know wasn’t imprisoned on the Ark was the piece on the Keyship. We don’t know for sure that another piece of him remained on Installation 07. Or if there is a piece of him on Installation 07, we don’t know if that piece successfully achieved metastability like the rest of him did.

And as far as Cortana goes, we don’t know if she’s truly rampant. Rampancy for a human smart AI is a death sentence. The Domain is allowing her to avoid that death. In that respect, she’s already been cured.