You can decide whether to have your profile set to public or available to Upwork users only. For your reference, here's what each option means for your profile:
Here's the help article about profile visibility. Thanks!
Here is my opinion:
You should choose the most public settings possible.
The purpose of using Upwork is to earn money by offering your services to a worldwide customer base of clients. The purpose of the site is NOT to maximize privacy.
ANYTHING you put on Upwork is on the Internet. You could accidentally set your settings to public. Or Upwork could have a glitch. Or a client could copy your information to a blog post or tweet that goes viral.
So I consider the concept of "private" profiles to be illusory. If I am concerned about privacy, I think it is safer to make everything about my profile totally public. And then be mindful about what I post.