Evidently I cannot follow your argumentation, the key question is - what did Bernadotte know, did he know more than Davout, more than Napoléon himself?
This is in my view most unlikely.
He had his orders - he had to move to Apolda via Dornburg, or in case he deems fit to march via Naumburg, but Napoléon expected him to be at Dornburg already.
As pointed out - Davout ran accidently into the Prussian main army.
In case there was a request of Davout to Bernadotte - hypothetical - what could Bernadotte do? Even Napoleon did not believe the first hand report of Davout that he fought the Prussian main army - he was accused to have had double visisons.
So Bernadotte is stuck with his units at the defile of Dornburg - he would have to believe that Davout's report is right that he faced the Prussian main Army, he had to turn around, re cross Dornburg and then approach Naumburg and then the defile of Kösen and then sent his units into action.
Ultimately he would be too late to do anything, he would not even cut the line of retreat of the Prussian Army.
Béraud has a nice map in his superb volume 2 about Napoleon's art of war - showing the positions of the various units, there is only one good road from Dornburg to Apolda, from there Bernadotte could have move to the aid of Davout - via Eckartsberg (the original name of the battle) - or he could re - cross the Saale , try out the crossing at Camburg (which was deemed much more difficult than Dornburg and already rejected) - march to Naumburg, march to Kösen - march to Hassenhausen.
The army as such did not condemn Bernadotte at all, it were he lackeys of Napoleon who build up Bernadotte (after he truly realized that he completly misjudged the position of the Prussian main army) as a bouc - émissaire.
I read recently for example the memoires of Vigo Roussilon, he was with Dupont, no accusations against Bernadotte what so ever.
Those accusations were constructed post mortem by Napoleon and Berthier to cover their mistakes - because the army well asked, why was Davout sent against those odds alone??
Petre is of no use and indeed one of the sources who accuse Bernadotte without any substance, and was duly copied by Chandler.
When defending Bernadotte - I look at the original orders, I look at the map at what position Bernadotte was, I take into account his knowledge at that time and look at the map what alternatives did Bernadotte have.
John Cook and Robert Ouvrand wrote already two very good articles on that topic, Titeux even better.
I am leaning a bit into the direction of the argumentation by Bill Haggart (Bonnal) - that Bernadotte shouldn't have stopped his march to Dornburg due to the afternoon orders. This decision, was in my view - a bit unlucky.
Otherwise I cannot see any fault - nor bad will - nor any treachery which Bernadotte was accused and still is accused.