Learn Turkish: Zihni bulanıktı ama hemen uyanmalıydı. - His mind was blurry, but he had to wake up immediately.

The dictionary form is zihin (mind). When a suffix starting with a vowel is added to certain two-syllable Turkish words (often body parts or Arabic loanwords), the second vowel drops. So, zihin + -i (his) becomes zihni. This is a common rule called vowel omission (ünlü düşmesi).

How could we rewrite this sentence to use the o kadar ... ki (so ... that) structure taught in this lesson?

You could say: Zihni o kadar bulanıktı ki hemen uyanmalıydı. (His mind was so blurry that he had to wake up immediately.) By replacing ama (but) with the o kadar ... ki construction, you change the relationship between the clauses: his blurry mind becomes the exact reason he felt such an intense need to wake up.

How do the suffixes in uyanmalıydı work together to mean 'had to'?

It combines the verb root uyan- (wake up), the necessity suffix -malı (must/should), the buffer letter -y-, and the past tense suffix -dı. While uyanmalı means "he must wake up", adding the past tense changes it to a past obligation ("he had to wake up").

Is bulanık only used for abstract mental states?

No, it literally means "blurry", "cloudy", or "muddy" for physical things (such as bulanık su for muddy water, or having blurred physical vision). Using it for a "blurry" or fuzzy mind is a very common and natural metaphor in Turkish.