Your problem is a simple typo:
array($this, 'manage_post_columns', 10, 2)
VS.
array($this, 'manage_post_columns'), 10, 2
I guess you see the difference
Your problem is a simple typo:
array($this, 'manage_post_columns', 10, 2)
VS.
array($this, 'manage_post_columns'), 10, 2
I guess you see the difference