AFAIK, only by symptoms. If https fetches work and websockets don't, that's a sign. HSTS and assorted reporting can help a bit in aggregate, but not if the corporate MITM CA has been inserted into the browser's trusted CA list. I don't think there's an API to get certificate details from the browser side to compare.
A proxy may have a different TLS handshake than a real browser would, depending on how good the MITM is, but the better they are, the more likely it is that websockets work.
A proxy may have a different TLS handshake than a real browser would, depending on how good the MITM is, but the better they are, the more likely it is that websockets work.