Action might be required, hypothetically speaking, should interest rates rise to unacceptably high levels in response to the large-scale issue of government bonds, or if there were fears of bottlenecks in the flow of funds, or financial system instability in the process of structural adjustment.
Acting within their own mandates, the two policies can be mutually reinforcing. Stabilisation of the economy after the pandemic shock is a great example of this! However, in times of high inflation and slowing economic growth - that put low-income households in a particularly difficult position - mutual policy support is a greater challenge.