UK CoV2 infection rates among fully vaxxed are higher than those of unvaxxed ≥30

This question clarifies what exactly is the denominator. It is the population of that age group and is not stratified further by vaccination status. So this will naturally bias as more people get vaccinated within an age group.

This is an incorrect interpretation: "If I am an individual who is not vaccinated I will be less likely to be infected than someone my age who is vaccinated."

This (I think) is a fair interpretation: "If I am an individual who is infectious I am more likely to be vaccinated." While technically correct, how meaningful is it on it's own when we know more people are in the vaccinated group?

To roughly compare outcomes within an age group between vaccinated and unvaccinated people you'd need to additionally account for proportion of vaccinated status at that date. I may followup with those adjustments attempted.

I think its possible that the OP twitter author may be pointing out that there are issues of diminishing returns and questions of whether a mandate should be supported when you are more likely to be exposed to the virus by someone vaccinated vs not. I don't think I can quite tell if this argument stands on its own but I think there are far greater reasons to not support mandates.