Yes it hydrolyzes and therefore you have to add excess of carboxylic anhydride depending on the degree of N-acylation which you would like to reach. See attachment

Experimental Preparation of the N-aliphatic and Benzoyl Acyl Chitosan Derivatives The N-acylation of chitosan with the acyclic anhydrides was carried out in a binary solvent mixture of 1% AcOH/DMF (1:1 v/v). The addition of DMF helped dissolve the anhydride in the aqueous medium. An equal amount of the co-solvent (to that of AcOH) was added to maintain chitosan’s solubility in the medium, thus influencing homogenous experimental conditions. To minimize the possibility of depolymerization and the occurrence of side reactions, the reactions were carried out at room temperature. The experiments were conducted for 24 h. Prior to precipitation, the N-acyl products appeared as white or tan viscous solutions. Using 15 % NaOH for precipitation, the pH of the solutions were increased to pH 9. To remove excess base, the precipitates formed were first filtered and then washed with water until the pH of the filtrate was adjusted to 7.

Generally speaking, anhydrides are highly reactive derivatives of carboxylic acids. Lauric anhydride (or doodecanoic anhydride) is not an exception to this rule. Continuous exposure of an anhydride to moisture will eventually cause its transformation back to the carboxylic acid precursor. Deliberate addition of water or water in the presence of even a weak acid (such as acetic acid) will cause the hydrolysis of the anhydride in a shorter time.

My suggestion is to try dissolving chitosan in another solvent (other than CH3COOH) and to try avoiding an aqueous medium in the intended synthesis.

Jürgen Wintner, Nizar Matar thank you so much for your answers! Nizar Matar can you recommend another non-aqueous solvent for Chitosan? I didn't find one yet.

https://www.researchgate.net/post/How_can_I_dissolve_chitosan_in_organic_solvent