Unfortunately this sounds all too familiar as I am having very similar experiences with 13 Beta2.
I had the same SD Card experience where the SD Card would simply disappear and any apps or data that resided on the card be unavailable until the next restart (on rare occasion, it would take multiple restrarts before the card was recognized and access to the contents restored).
I also experience extended reboot times and thought maybe the two issues were related.
As a long term test, I removed the SD Card and did a factory reset. While there seemed to be some initial benefit, soon the long reboot (approaching and sometimes exceeding 5 min) has again become the norm.
For the black screen problem, I noticed that the phone is still responsive and often the screen’s backlight will turn on. Though the screen stays black, I can unlock via fingerprint and with the auto-rotation option enabled and a little luck that the opened app of the now unlocked phone is responsive to screen orientation changes, the transition between horizontal and vertical will turn on the screen and things get back to normal. The trick doesn’t always work but does save me from a few reboots.
Finally (and this post is getting a little too long) my poor T2e really struggles when I’ve got Android Auto and Waze and an audio streaming app on at the same time… That’s A LOT for the beta release and somedays it works OK, sometimes it limps along as best it can and sometimes it gives up and takes a long reboot break.
That’s where I’m at.
-PlantP