OMEMO leaks plenty of metadata; most things other than message contents are left unencrypted. Many of the mature XMPP use different OMEMO versions (which can be hard to tell when the client doesn't clearly state the XEP versions, like Snikket). I spent 40 min scouring Snikkets website and source repo without any clear way to determine what version of OMEMO they bundle. I said OMEMO+XMPP because no matter how secure your protocol is, the actual implementation by your largest userbases determine real-world security.

And lastly, just because "serious institutions and governments" use it doesn't make it more secure. Many European governments use Matrix, and that has even worse security, breaks forward secrecy, doesn't encrypt basically anything other than message content, etc. Many governments have critical systems that run unpatched Win 7 or older. My point is that security is independent of adoption.