Is logistic regression or survival analysis most appropriate in this case?

We compare the impact of two methods of bariatric surgery on patients’ comorbidities. The hypothesis is that comorbidities disappear much more after one type of bariatric surgery than the other. The patients were operated on between 2010 and 2020 (and the analysis will focus on patients who have comorbidities associated with their obesity). They were contacted in 2021 to reassess their status, whether or not they still have their comorbidities. I am wondering what method I should use to compare the two groups in terms of improvement in comorbidities. I first thought of a survival analysis because the patients do not have the same observation time after their bariatric surgery, but with survival analysis, the time to event could be slightly or strongly wrong because we do not know exactly when the event (i.e. disappearance of the comorbidity) has occurred. For example, a patient who was operated on in 2011 would have a time to event of 10 years (as I have no information between his operation and his appeal) whereas he may have recovered much earlier. I then thought of doing a logistic regression with adjustment on the year of operation, since the last information on each patient is in 2021. If I am right, the logistic regression, with an adjustment on the year of operation, will allow to compare the two groups in each year subgroup.

Since it is ultra important to use a well-performing comorbidity score that captures the number and severity of comorbidities, and because time is important, the appropriate statistical design is a longitudinal analysis of the continuous/ordinal comorbidity score. See for example this.