I don't think you can draw the conclusion you want to draw from this chart. In order to see the impact of restrictions, you would have to overlay the case loads these 3 groups in a no restriction situation and compare the slope of the lines and the scale on the left axis. Convenient for you, we only get one shot and so the alternate scenario data isn't available for comparison.
As to why the rate of vaccinated cases are rising faster than unvaccinated...
We know the vaccines are less effective vs Omicron. Breakthrough Omicron > Breakthrough Delta. The vaccinated and partially vaccinated group was doing fairly well in early December against Delta, but around December 15th something changed. Presumably, the impact of Omicron. For the unvaccinated group, it appears that Omicron did not change their level of protection Delta vs Omicron, the slope at this point of the purple line did not change. The other part, I suspect is still behavioral. This is why the slope changed for all three groups at basically the same time around Dec 22nd. Even careful people got together with their friends & family for the holidays. I assume careful people are more likely to be 'fully vaccinated with no previous infection,' so they were more at risk for infection than at anytime after they had been vaccinated and bad for them, Omicron also attended the gathering. For a lot of people their "risk" profile changed significantly during that week unlike for the unvaccinated or even partially vaxxed who presumably stopped being careful a long time ago. If Omicron had hit in January, after people visited the family and the careful went back into hibernation... when even people-loving folks are willing to take the time to be a temporary homebody after gathering overload, I wonder what the slopes would look like.
All this chart really shows, IMO, is what we already know. Omicron is more infectious and vaccine-immunity evasive than other variants. You'd be better off making the case that infection-immunity is better* than vaccine-immunity at least against Omicron. However, the implication is that in order to disrupt Omicron infections you would need to do MORE than what was done before to see the same impact. Is anywhere doing more?
* Only talking infection protection. Once we add in "damage while infected" obviously vaccines have a huge advantage. I'm not sure how many people wouldn't trade a little less protection against a future variant to avoid hospitalization, death, potentially long-COVID for past and future variants.