Deaths lag cases. Take a look at the graph to clearly see this in the red and blue plots.
Obviously hospitalizations are rising rapidly which precede the the deaths.
Let's do some math...
Let's say that Omicron is 70% less severe than Delta (based on U.K. and South Africa data for hospitalizations) but the percent of deaths for the number hospitalized remains about the same (remains to be seen). Cases go up with Omicron by over 4X what was seen with Delta (as seen in multi-countries).
Now for some math. Only 3 people are hospitalized for every 10 we saw with Delta per the number of cases. But the number of cases is 4 times as great with Omicron compared to Delta. So the total number of hospitalizations for Omicron based on the increased cases can be viewed as 3 people but 4X the cases yields 12 people severely ill with Omicron taking up beds even though Delta only had 10. A portion of the hospitalized will die (at similar rates). All of this means the concerns about hospitals being overwhelmed with increasing numbers of Omicron patients is quite correct (and is already being seen).