there is nothing to wonder, in case one is studying the available source diligently - and I am not alone on this opinion - Bernadotte just fulfilled to the letter the orders issued by Boney himself.

Bernadotte was ordered to be at Apolda at the day of the battle, despite the terrible terrain he had to overcome - he did this and cut off the retreating Prussians of Auerstedt defeat their line of retreat - which was a major contribution of the unhappy retreat of the Prussian Army.
Neither Boney, nor Davout - nor Bernadotte did know that the Prussian main Army was at Auerstedt - the concept was, it was at Jena, so Bernadotte was not inactive at all - he did what was requested - but then a scapegoat - the usual Boney lies - had to be found for the mistakes of the Etat - Major - and the excuse that the clairvoyant Boney was wrong with the location of the Prussian main army.

Indeed Bernadotte did much more harm than being at Apolda than being stacked behind Davout's corps at Hassenhausen, a look at the map would show this.
Also then Bernadotte was given the important task to persue the Prussian main army, that clash at Halle proves again his skill as extraordinary general and unit leader.
Bernadotte, as well as Marmont, as well as Dupont, as well as Ney, as well as Grouchy - are convenient scapegoats of Boney propaganda in first place and Boney apologists post mortem Boney.

A good start to gain information - would be Foucart, the essay of John Cook here on the series https://www.napoleon-series.org/military/battles/c_bern.html , here the second part of a great discussion we had on Markus Stein's web site - enjoy

http://forum.napoleon-online.de/archive/index.php/t-48.html