It's an unreleased OST called Soul Society by Bleach's music producer, Shiro Sagisu.
The relevant (YouTube link).
Quote from OP:
I found it. Can't believe I found it. It was so hard that even in the comments people say that found it by mistake and was not on purpose. I spent 5 years looking for this and I found it. https://www.youtube.com/watch?v=gntBKXOrppI (YT: #10) BLEACH OST - Shiro Sagisu - BL_93 (Soul Society)) for anyone in my position