Yes, unfortunately this issue in Sonoma still persists. I keep posting updates to my bug report to Apple, but so far there has been no response from them.
No, it's not related to SSD.
My further research has shown that apart from ~/Library/Containers, other privacy-sensitive folders like ~/Documents, ~/Desktop etc. are also relatively slow to open - but only on their root level - and their subfolders are opened quickly, so no slowdown is noticeable. By contrast, all recursive subfolders of ~/Library/Containers are slow to open.
The slowdown occurs due to an expensive security check that macOS performs on each call to open a subfolder inside ~/Library/Containers. The security check may involve calculating the hash of the calling executable, because the duration of the delay clearly depends on the calling app's file size. Besides, there seems to be only one system thread that performs the check - so that if many threads are asking to open a folder simultaneously, they have to wait for each other in a queue, which creates a real bottleneck in performance.
All in all, it seems that this new "security feature" of macOS Sonoma was implemented without much thought about performance. Not to mention that when the user grants the "full disk access" to an app, the security check for it must not occur at all, but it does occur, unfortunately.
I really hope Apple will notice the problem.