I'm on the same, wont be nice and wise from ESET to offer Beta releases, no warranty or large support for that but following as Apple Beta Program, subscribers, etc ?
I'm on Ventura 13 Beta 3 and really did not noticed that ESET was not running until miss the upper icon
I did not recall a warning and it wasn't deleted ... it's showing in Privacy & Security and all enabled, but it just cant run.