Jews have been writing, adding to the pool of Torah knowledge for thousands of years. How many complete or partial works do we have accessible, even by any means today?
I would divide the answer into 2 periods.
Until about 50 years ago, the list of printed Torah literature was small enough for their bibliographies to fit into a 2-volume book - namely שרי האלף (Sarei Ha'Elef) - Masters of Thousands - referring to the 1,000 year period from the time the Talmud was sealed until the book was printed.
It was printed in 1959 in New York and then again in 1984 with all the recent additions. Since then people have been trying to keep it updated.
I can't find a "total number of books" that it contains, probably since it would depend on how you (want to) count similar editions, making the number meaningless.
More details (in Hebrew) can be found in its WikiText entry.
The second period started "recently" - somewhere before that 21st century began, when publishing became "trivial"; get a laptop, type (or copy/paste) in your spare time and once you have a few hundred pages then for a few hundred bucks you can publish your book.
Since being an author of a Torah-subject book (i.e. Sefer) is considered a prestigious achievement, it seems to have become the goal of many a Kollel-man to join that club.
As a result, there are multiple new Seforim (plural of Sefer) published daily!
And that's in the world of the Sefer, before we get to the grey area of publication appropriate for the religious home like Kosher novels, Chasidishe tales, Kosher Comic Books and similar.
At the moment you can access 90,200 Seforim (as scanned pages of the original, and searchable) if you have Access to Otzar haChochma - and they claim to be adding 5,000 Seforim yearly!
Disclaimer - I have never used Otzar haChochma and am not affiliated with them, I just see their ads occasionally and they are a good example of the scope of what the OP is looking for.
Point being that as you read this, the list grows.