I see mine *but* I don't think it showed up in the "My product downloads" tab until *after* the SDA succesfully accepted my Download Access and Activation Codes.
Were you able to do those two things? If not, you probably should not expect to see it there.
I had a similar problem last year (when I tried to 'grace-period-update' C9 to C11) and the issue was that my copy of C9 had been updated to C10 *but* still remained in my account. SB told me that it should have been removed b/c it was used to upgrade to C10. And so I had to pay to upgrade to C11 (from C10).
Could this be the cause of your problem?
A potential workaround suggested on the Cubase Forum is to "...copy the Synthengine.vst3 to the Cubase 12 VST3 folder..."
Apparently this works for Mystic, Prologue and Specter, but not for LoopMash.
https://forums.steinberg.net/t/cant-find-prologue-mystic-spector-in-cubase-12/769948/5
I watched a few of the 'Top N Reasons to Update Now' videos, but they largely replicated the information provided on Steinberg's website.
The video below, in contrast, provides detailed information on many of the new and useful functions.
I honestly don't know, but I recall someone asking the same question this morning on the Cubase forum and I think the answer is 'no.' That is, you should be able to run both at the same time.
I recall reading it here but really don't remember given that I've reached a state of information overload.
https://forums.steinberg.net/t/cubase-12-out-now/769760/41
Great video (and surprisingly useful piano). Had I not watched it I would likely not have even installed it because, like you, I thought who needs another felt piano?
Track-level ARA functionality and Audio Warp directly in the Track Editor are big improvements which finally allow us to easily align any type of event across tracks.