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Collins dictionary says:
If you are wary of something or someone, you are cautious because you do not know much about them and you believe they may be dangerous or cause problems.
I found some examples in dictionaries.
Brands need to be cautious about which environment they place themselves in.
They were very wary about giving him a contract
What would be the difference between wary (of/about) and cautious (about)?
An interesting question. The two words are synonymous for the most part. However, wary has a bit more of an emotional component in it, a feeling of reluctance to do whatever one might be wary about doing. Cautious is more of a carefulness based on reason.
From the Merriam-Webster definition of cautious (the synonym discussion halfway down the page):
Cautious implies the exercise of forethought usually prompted by fear of danger. ⟨a cautious driver⟩ ... wary emphasizes suspiciousness and alertness in watching for danger and cunning in escaping it.
