I've learned the phrase'see straight'. According to Longman Dictionary, it means: see clearly (this is the link: https://www.ldoceonline.com/dictionary/think-see-straight). So it is correct and natural to say: 'The thick fog prevented me from seeing straight anything.'? Thank you in advance.
The direct object pronoun anything should come before the adverb straight.
I can't see anything straight.
For your example, though, the adverb clearly fits better:
I can't see anything clearly.
The use of see straight is figurative, as shown by all the examples at your link.
The non-figurative use of seeing through fog is better conveyed by clearly.