I would suggest that for pre-Omicron variants we probably do have enough information. From memory there was something like a factor of 7 difference between vaccinated and unvaccinated across the board - likelihood of contraction, likelihood of hospitization, likelihood of requiring ICU care. I would be surprised if that did not also extend to likelihood of transmission.

To be clear: solely in the context of Omicron, Fjallstrom may well be spot on. But it is probably not yet the case that "the virus" and "Omicron" can be used interchangeably.