- But they didn't account for the treatment for Covid as being a possible cause for the difference.
- Nor - conveniently? - is there mention of vaxinated vs non-vaxinated. Boosted vs non.
- The final check would be those who knew they had Covid vs those who were asymptomatic. Stress is a powerful force. Those aware of having Covid may have stressed more, which is known to effect the immune system, weight gain, etc.
To reach 'causation' would require intentionally giving your experimental subjects Covid-19 (and in a way that didn't result in them knowing they'd had it!), and that's unlikely to pass muster with the ethics review board.
It reports the correlations found - those that had a COVID diagnosis (with no prior diabetes indicated) had a greater chance of developing diabetes.
It doesn't report that those vaccinated (with no prior diabetes indicated) had a greater chance of developing diabetes NOR does it report a great many other potential relationships.
The probable reason for that lack of reporting is the absence of pattern being present in the data ... it's reasonable to assume that multiple correlations across fields in the EHRs were run (including against vaccination status).
If you suspect a vaccination effect you can always look to Australian health studies - the country has decades of world class near total population records for the entire country and had a near total COVID vaccination program with multiple doses.
Any effects would clearly show up in the before and after M&M stats of 25 million people.