After some digging for more evidence I found that some studies supported the possible benefits of budesonide for treatment of pneumonia in children.

• Li B, Han S, Liu F, Kang L, Xv C. Budesonide Nebulization in the Treatment of Neonatal Ventilator Associated Pneumonia. Pak J Med Sci. 2017 Jul-Aug;33(4):997-1001. doi: 10.12669/pjms.334.12907. PMID: 29067081; PMCID: PMC5648980.
• Shen H, Zhao X, Xu L. Meta-analysis of the efficacy of budesonide and ambroxol hydrochloride inhalation in children with pneumonia and their effects on inflammatory response. Heliyon. 2023 Oct 19;9(11):e21105. doi: 10.1016/j.heliyon.2023.e21105. PMID: 37954384; PMCID: PMC10637922.