Actions speak much louder than words, to use a time-worn phrase. Bernadotte knew because Davout undoubtedly told him, that the Prussians had driven in Davout's outposts on the afternoon of the 13th and that there was a Prussian advance behind that action. That is why Davout was alerted and when Davout received Napoleon's 2200 13 October order at 0300 on the 14th he gave Bernadotte a written copy. The two corps (I and III) were practically co-located and the order to march with Davout was very clear.

Bernadotte chose instead, to comply with the older order to march to Dornberg instead, effectively leaving Davout on his own and keeping his own corps out of action on 14 October.

That's what happened and Bernadotte had to know that both the main army and Davout were engaged as he marched as the smoke from the actions would have been visible from his march route.

The bottom line is that Bernadotte did not do his duty, the only real question is did he do it purposely or because he was incompetent. Looking at Bernadotte's career up to 1806 he certainly was a competent officer and commander. So, that leaves the result that he did it on purpose.

As to modern authors, it is the historians job not only to 'tell the tale' of what happened in the past, but to conduct historical inquiry to try and find out why, the 'why' being the most important conclusion to make. So, I disagree with your comment on modern authors.

Here is a comment from Phipps, Volume V, page 27 on Bernadotte's character regarding being a commander and accepting responsibility:

'Another annoyance to Jourdan was the formation of the Armee d'Observation. His own army had been organized in six divisions...but in February 1799 the two left divisions...went to form the Armee d'Observation under Bernadotte. This army, often miscalled the Armee du Rhin, was supposed to have flanked the left of the Armee du Danube. It only existed from February to April 1799, its personnel being mainly drawn from the Armee de Mayence and then being absorbed back into that army, which had meanwhile become 'Danube.' Its objects were to blockade Mannheim and Phillippsburg, to furnish the garrisons for other places on the Rhin, and to support the operations of Jourdan and his army be demonstrations on the Main and the Neckar. It was to have had, including garrisons, some 48,000 men, but it was actually very weak; the divisions of Dallemagne and Laborde formed its cadre. Bernadotte came from Paris to command it. This appointment of Bernadotte was made in a curious way. On the morning of the 5th February 1799 he was nominated, the appointment being cancelled at noon and made again that evening. Next, on the 10th February he was nominated to succeed Joubert in the command of the Armee d'Italie, and Schauenbourg, the former commander of 'Helvetie', now, I think, with the Armee de Mayence as Inspector-General of the Corps du Haut-Rhin, was posted to 'Observation.' Finally on the 27th February Bernadotte was again appointed. These changes were caused by difficulties about the command in Italy, which Bernadotte refused...He had been longing for an independent command, and now took this army although he was to act under Jourdan, thus occupying a lower position than if he had gone to Italy. Perhaps we may see one of Bernadotte's characteristics in this: wishing for a command but drawing back from what must be arduous, he takes one on which the main stress of war is not likely to fall.'

Sincerely,
K