Here are the 'pieces' that you posted.
"The glory and good fortune of France have been and always will be my first task; and your Majesty will always find in me a faithful subject animated by the love of his duties and full of confidence in his enlightened justice." -"Mťmoire de M. le Marťchal Davout, prince d'EckmŁhl, au roi"
"The wish of Frenchmen, consecrated by the act of the Senate, the adhesion of the Legislative Corps, of the high dignitaries, of the principal courts of justice, of the communes and of the army, has abolished the imperial government in France and has called the Bourbon dynasty to the throne of France.
We therefore swear to our king,
Obedience and Fidelity
By order of the marshal Prince d'Eckmuhl."
"Released from our oath by the abdication of the Emperor Napoleon, by the acts of the Senate and by the wish of all France, we will consecrate our lives to the defence of the descendants of Henri IV, of Louis XIV, and of our dear country."
"I beg your Royal Highness to welcome with kindness the general baron Delcambre, charged with laying at the foot of the throne the assurance of our fidelity and to graciously accept the homage of the profound respect etc."
signed Prince d'Eckmuhl.
These were all written before he returned to France, and oaths aren't given in writing, at least not by soldiers. Davout was encouraging his troops to keep discipline and return home. I don't see 'enthusiasm' for the Bourbons, just the usual directions by a commander to his troops. What did you expect him to say-resist the new government of France? Please...
Again I highly recommend Gallagher's biography of Davout especially the last few chapters on Hamburg, the Bourbons, and Davout serving Napoleon again without hesitation in 1815.
From page 298:
'Davout remained out of favor throughout the First Restoration. His Memoire du Roi was accepted by Louis XVIII as a satisfactory explanation of his actions while in command in Hamburg. Nevertheless it was well known in all quarters that the Marshal had been one of Napoleon's staunchest supporters, and that while he had accepted the white flag of the Bourbons, it had not been until he had received unquestionable proof that the Emperor had been removed from the scene. Furthermore, unlike the other marshals, he did not seek employment with the new government. Shunning Paris, he was quite content with putting his own affairs in order and seeing to the management of his estate at Savigy while at the same time enjoying the reunion with his family. His career as a soldier would have ended at this point had Napoleon not reappeared in France in March 1815.'
From page 299:
'Marshal Davout had not taken service under the Bourbon regime. His acceptance of Louis XVIII was the acceptance of the de facto government of France. Now that the king had fled the capital, Davout considered his government no longer to be that of France, and he had no reservations about offering his services to the Emperor...'
Material needs to be taken in context...