This paper from Jan 13 has very interesting design.
They used VA data in US. It does not cover omicron.
Studying breakthrough infections would be interesting to read about (by patients).
I reviewed this list: https://github.com/ohdsi-studies?q=covid&type=all&language=&sort=
Is this study https://github.com/ohdsi-studies/Covid19VaccineEffectiveness progressing ?