I think it is worth digging into the meanings of "vulnerability" and "confidence" here.
I think "confidence" is rooted in the belief that "whatever happens, I'll be able to handle it. I'll be okay." Showing confidence is externally-emoting as if you believe that to be the case.
Vulnerability...I'm less sure of. I think it is the ability to be wounded. By being vulnerable, you reveal information which someone else could use to ridicule you. Patrick Lencioni's work on organizational health refers to vulnerability as a key piece of building trust[1]. How does it work? By showing that you expect that people hold a social norm against ridiculing people for the thing you reveal. That you are willing to pay a cost for that social norm. I think when people use the word "vulnerability", they mean sticking your neck out for a social expectation of compassionate collaboration -- norm-building vulnerability.
And that sort of vulnerability is compatible with confidence. If they do ridicule you, then you've learned what sort of person they are and you have the power to respond accordingly.
But I think its easy to confuse norm-building vulnerability with another vulnerability: insecurity-revealing vulnerability. This is where you present something that could genuinely hurt your sense of belonging -- Information which you think others could present as evidence that you should be ostracized from a group. For example, a man in a homophobic environment who reveals that he is bisexual. How should a man express these sorts of insecurities? By default, he shouldn't. He should hide them until he can find a supportive community. Unless he's with someone he already trusts or a mens' meeting of Alcoholics Anonymous. Don't express insecurity-revealing vulnerability.
[1] https://www.tablegroup.com/newsroom/news/vulnerability-endea... is an example, but he talks about the concept in The Advantage and his novels.