Exactly, the attack rate of vaccinated individuals who are infected is significantly lower.

All the current data suggests something very different.

https://www.forbes.com/sites/jemimamcevoy/2021/08/06/fully-v...

I can't find any source in there suggesting a lack of effectiveness. The underlying source linked by the article mentions a reduction of 80% in symptomatic disease, which is responsible for most transmission. I can't find anything very recent, but here's an analysis that takes Delta into account:

https://assets.publishing.service.gov.uk/government/uploads/...

Finding 80+% protection against symptomatic disease and ~40% reduction in onwards transmission, from three different modelling groups.

Those estimates are based on modelling with assumptions to fill in missing information. Significant is the assumption of little waning immunity.

Current data trends don't look so optimistic.

https://dailysceptic.org/2021/08/22/latest-phe-data-shows-va...