You can continue to monitor for signs of inflammation and liver function following cholecystectomy. Also monitor for dysbiosis, nutritional status, and wound healing.
Remember the gallbladder is just a storage depot for bile- the liver produces bile and can continue to release it directly into the small intestine when needed.
Since the gallbladder was removed, then it may be likely that biomarkers of inflammation and oxidative stress would decrease.
However, you can monitor biomarkers for persistent inflammation including CRP/hs-CRP (Jansen 2018) and neutrophil:lymphocyte ratio (Diez-res 2021). You can also monitor liver biomarkers in case of more extensive liver involvement, including AST, ALT (Rajab 2020), albumin (Mok 2014), and GGT (which can give you an idea of ongoing oxidative stress and increased need for glutathione).
If they had a course of antibiotics then you want to monitor for dysbiosis including C-difficile and Candida overgrowth. If they had an open cholecystectomy monitor nutritional status, wound healing, and immune function.
References
Díez Ares, José Ángel et al. “Can inflammatory biomarkers help in the diagnosis and prognosis of gangrenous acute cholecystitis? A prospective study.” Revista espanola de enfermedades digestivas : organo oficial de la Sociedad Espanola de Patologia Digestiva vol. 113,1 (2021): 41-44. doi:10.17235/reed.2020.7282/2020
Jansen, Stefan et al. “Advanced gallbladder inflammation is a risk factor for gallbladder perforation in patients with acute cholecystitis.” World journal of emergency surgery : WJES vol. 13 9. 20 Feb. 2018, doi:10.1186/s13017-018-0169-2
Mok, K W J et al. “Is C-reactive protein a useful adjunct in selecting patients for emergency cholecystectomy by predicting severe/gangrenous cholecystitis?.” International journal of surgery (London, England) vol. 12,7 (2014): 649-53. doi:10.1016/j.ijsu.2014.05.040
Rajab, Ibraheem M., et al. "C-reactive protein in gallbladder diseases: diagnostic and therapeutic insights." Biophysics Reports 6.2 (2020): 49-67.