I am very interested to know if and when there will be a 3.4 release mostly because we are using concurrent use licenses (yes, aware they will go away in about a year) and will likely need to upgrade the ArcGIS license manager software at the same time.. we also need to upgrade to version 2024.0 to officially support 3.3, but I'm hesitant to do that if 3.4 and 2024.1 or 2025.0 will be released soon.. I'd rather wait for that.. any intel or insight would be greatly appreciated! I also found the following link to a list of previous release dates which at least as of today is more up to date than the wiki article mentioned elsewhere in this thread: FAQ: What Are the Build Numbers for Releases of ArcGIS Pro? (esri.com)
I heard from Esri support that 3.4 release is expected around end of November (hopefully sooner), and yes there will be a new ArcGIS license manager as well (presumably 2024.1) for concurrent use licenses.