The digital signatures are 𝘱𝘳𝘰𝘰𝘧 that the sender in a transaction was the rightful owner of the coins being sent, but they don't 𝘥𝘦𝘵𝘦𝘳𝘮𝘪𝘯𝘦 the ownership. They're derived from the private key (which 𝘥𝘰𝘦𝘴 determine ownership) with a cryptographic function, so that it's easy to verify that the signature is correct, but practically impossible to use it to figure out the private key.

So they are visible to everyone. That way, anyone can fully audit the blockchain, but that does 𝘯𝘰𝘵 make your bitcoin vulnerable to theft or anything else.