The usage of the word "hype" is correct here. Sounds very natural!

Think of hype as another word for 'excitement'. If you think you could use excitement in a phrase you can probably substitute hype as it's has a similar meaning, hype just implies that advertising is involved in the excitement. Your examples work, I would lean towards 'around' but either is fine, you can also use 'for' as in 'there is a lot of hype for the new Star Wars film at the moment' etc.

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