The Supplement is a continuation of the Official Records. They just gathered up more reports that weren't included in the original Official Records and made another addition.
(They also included the Event Records of what each Company wrote on their bi-monthly rolls. This is handy if you are trying to following one specific Company, whereas most places on the WEB just give a Regiments service, and not all the Companies of that Regiment did exactly what the the Regiment did.)
As to the 'accuracy' of the Official Reports - you must keep in mind that these reports were written by Commanders that did not want to look bad. Seldom do you get a exacting viewpoint of what happened. I have found that they are the best overall writing of an event, as Confederate reports are hard to find from Missouri. The best bet is to take the reports, any newspaper articles (which are notoriously inaccurate), county histories (which are even more inaccurate) and personal letters and diaries (usually the best - but limited to that persons involvement) and sift through what is consistent throughout and make your own judgment.
Also the Government selected which reports to include in the Official Reports. (They did not include the reports from their loss at Newark.)
In regard to Manning's diary - what are the dates it spans and where did the unit tend to be located? I might have some interest in the weather reporting.
I have recently moved and the old town I lived in had a copy of the Supplement, so it was easy for me to look things up in it. The new town does not appear to have them, but I am looking around to nearby libraries.