Estimate the period effect using logistic regression

I am currently reviewing a paper that estimates the effect of the COVID19 lockdown on a medical outcome $Y$. $Y$ is a binary variable. The authors use patient-level data from March – May 2020 and from March – May 2019 and fit the following logistic regression model:

$$mathrm{logit}(Y_i) = alpha + beta_1 T_i + beta_2 X_i$$
with $T_i$ being an indicator variable for the periods 2019 and 2020, i.e. taking two values, and $X_i$ being a vector of covariates.

The authors present adjusted odds ratios to assess the association of the lockdown with the outcome variable.

I am a bit unsure whether a logistic regression model is appropriate for this type of data because the observations are not independent (i.e. they are clustered at two time periods). What other modeling options would be more appropriate? I would have tried an interrupted time series analysis if enough pre-lockdown and during-lockdown data was available. A generalized linear mixed model would not be very helpful if the authors are interested in the period effect, right?