I suggest to be more cautious in your conclusion that metformin reduced incidence of long Covid in the study you cite. Studies such as these are necessarily “messy”, and there are many statistical methods to make them “unmessy”. The problem with applying these methods is that they rely on assumptions that are often untrue, or they cannot account for information that is not available. In the study you cite, the authors, acknowledge the fundamental weakness in their study.

“Because the definition of Long Covid is rapidly changing, fluctuating symptoms are challenging to assess, and ICD codes lack specificity and sensitivity, the primary method for ascertaining Long Covid was participant-reported receipt of a Long Covid diagnosis from a medical provider.”

“Medical providers” will vary greatly in their training, knowledge, and experience, and therefore assessments, to arrive at a conclusion of long Covid. This is especially true because at the time this study was conducted there was a huge basket of symptoms that could be used to designate someone as having long Covid.

Studies such as these are interesting, but they do not rise to the level upon which to base a medical recommendation, IMO.