The public key is included in the script for spending UTXOs (inputs) so that anyone can verify that you do have the private key (an important reason why it is not a good idea to re-use addresses).
Sorry if this is a stupid question.
I have seen quite a lot of sites such as faucets and casinos keep reusing their hot wallet addresses. So, will reusing address pose any real threat on the bitcoin in that address? How dangerous would it be?