it is absurd for me to see such a topic as treachery discussed seriously as there was none whatsoever, Bernadotte got his orders and he executed them.
Berndotte took great efforts to achieve the goals set by Napoléon as can be read in the article of Titeux - link provided by Steve Smith.

Neither Napoléon nor Davout did know that Braunschweig was in front of Davout.
The initial order that Bernadotte could follow Davout - in case he was in the right position - was due to the speculation that a big part of the Prussian Army was in front of Lannes (true) and still a bigger part at Weimar (not true, there was only Rüchel).
This order would make sense if that would have been true but collapsed with reality when Davout did run unexpectatly into Braunschweig (Prussian main army).

When this did happen - Bernadotte was already miles away and due to difficulties of terrain - he had to put up much effort to reach Apolda. In case - hypotetical - he would have realized then, by magic (otherwise impossible) that Davout was in desperate fight with the Prussian main army, he would have to make a demi tour and follow the tracks of Davout - by that arriving much too late - and waste his time - or to continue with his original orders.

Those by the way can be read in the work of Foucart, the famous missing one is in - Gabriel Girod de l'Ain : Bernadotte (biography) and also the ovservations by Dupont - all support that Bernadotte did his duty but was later built up as scapegoat.

And I agree - what motivations should he have? In the following actions, like Halle Bernadotte showed excellent initiative and energy and was the thriving motor behind the persuit of the Prussian Army.

Others did behave much worse, letting escape Blücher who fooled them, but nobody would accuse Lasalle of treachery of course, which would be as absurd as accusing Bernadotte.

Serious study of original orders and looking at the map, let crumble all accusations against Bernadotte into dust.