I started using it to document the system (we didn’t have documentations of any sorts) and create our regression tests.
In this case, you should definitely use of any sort, which is correct (you could also use of any kind, or possibly of any type). You are effectively saying "We did not have documentation of even a single kind".
Although "sort" is sometimes found in the plural, it is in rather exceptional sorts of circumstance (like this one, where there are multiple types of circumstances). To say you had documentation of sorts is an idiomatic use of of sorts, meaning you had something that is barely documentation; this usage cannot be made negative, and doesn't work with "kinds" or "types".
You could probably get away with it with a definite article and relative clause:
We could not find clothes of any of the sorts sold elsewhere
Note also that in British and American English, documentation is an uncountable noun and should be left singular. I know some uncountable nouns in English become countable, e.g. Indian English "baggages", but I've not heard of it with documentation.
Therefore, you should write:
I started using it to document the system (we didn’t have documentation of any sort) and create our regression tests.