I have installed MacOS Ventura (MacOS 13.0 22A5266r) on my MacBook Air M1. I am pleased to say that Logos 9.14.0.0022 opens and appears to function normally.
As always, we can't expect Logos to make any statements or promises about MacOS Ventura until its full release in the fall. If the past is any indication, Logos will not even say they WILL support Ventura until its full release. This is important, too, especially if you have never installed beta system software: Logos will not provide formal tech support for unsupported systems. Thankfully the forums carry the majority of that load for most of us.
For the record, my MacBook Air is not my primary computer (that's a MacBook Pro M1). I won't install Ventura on my main computer until I am confident that Logos and Proclaim will function normally. I recognize the risk of using beta software and am fully prepared to take the time to downgrade if it becomes necessary.
I will finish sermon preparation today on the MacBook Air and report any issues I encounter. And I'm happy to answer questions about Ventura.