Is the statement by Ibrahim ibn Adham: "It is for me to worship Him as He commanded, and for Him to provide for me as He promised me" considered ill-mannered towards Allah, and what is the extent of its authenticity?

We have not come across any authenticated source for this story. However, it does not show any ill manners towards Allah; rather, it indicates the sincerity of its narrator and the strength of his reliance and certainty that his sustenance will not elude him. Sustenance is decreed, and Allah Almighty has guaranteed the provision for every living creature. This is not an imposition on Allah, but rather it is He, Glorified be He, who imposes upon Himself whatever He wills.