A much simpler explanation is that this is a side effect of the pandemic itself.

The timing of the vaccine roll out is of course related to the timing of the pandemic. So it's expected that we would see some loose correlation in timing between the different events related to the pandemic.

Things such as increase in mental issues and increased drug consumption due to loneliness, lack of medical care due to overflowed hospitals or loss of income etc. all took time to build up once the pandemic started. Just as it took time to manufacture and distribute a vaccine once the pandemic started.