Someone saying "hidden" makes me think of posts scoring -3 or lower, which are faded to make them harder to read - or of spoiler markup. Both things that hovering clears up.
Additionally, "hidden" implies that anyone can find them if they know how to, which isn't true - only mods, "10K" users, and the OP of the post can see them. With the exception of these users, the post is deleted. Even low-reputation users will have difficulty finding their post again unless they have a link to it (or if it's an answer, can find the question) as it's removed from their profile 60 days after it was created.
Also, I think that calling it a "soft delete" really isn't necessary... even in computer systems, deleted files can often be easily recovered provided they haven't been overwritten (and sometimes even then). Several dictionary definitions include mentioning that "deleted" implies simply "drawing a line through" text. This is an action that can certainly be recovered from.
I appreciate your concern and I can understand wanting to find better vernacular for this but I sort of wonder if it gets into a similar amount of hand-wavey-ness like the difference between "on hold" and "closed" (which are technically different from each other).
In my experience, very few experienced users say "your post is on hold"... even when it is... usually, we use the term "closed" for both statuses... particularly in our custom close voting reasons, which default to "I'm voting to close this question because..."
I don't think that calling these posts "hidden" instead of "deleted" is accurate, nor do I think that it's likely the term will be adopted widely... it might be used by the system, but getting the users to change what they say, particularly long-time users, would be difficult, particularly if they don't like the term, as for the reasons mentioned above.
There may be another word that could work but I don't think "hidden" is it.