I have a dataset that has missing values in baseline variables (t1) and in outcome variables (t2 & t3). Each individual has a unique ID and three lines in the dataset. I imputed these data via mice with a 2-level approach as recommended by van Buuren.

Now I have the dataset in long format and was wondering: how would I conduct a PSM that draws on the baseline variables and keeps the connection (meaning the other two lines of the treated and matched unit) between lines? Does anyone have experience in this? Goal is to conduct DiD-Analyses in the matched sample.

This is a pretty basic question, so I did not have an idea yet on what to even try. I conducted several analyses with MatchThem in wide-formated datasets, but have no experience in long-formated datasets.
I had a look at different (answered) questions here on Stack Overflow, but most of them work with STATA and without imputed data.