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It's an unreleased OST called Soul Society by Bleach's music producer, Shiro Sagisu (YouTube).

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