yup same. I had the same concerns. I had very little interaction with baby over the one month. whenever baby cries and I pick her up he cries life and death, nanny is quick to come and grab baby away and he calms down pretty quickly. Nanny is gone for two days now. The first day baby is pretty cranky whenever I carry, but it seems 2nd day it got better. i think baby will get used to you pretty quickly as you will be their main caregiver from now so don't need to worry. If you still worry, then have more interactions with baby throughout the day, ask nanny to learn how to change nappy or bathe your baby to have more interactions with him before your nanny leaves so baby won't see you as a stranger when she leaves.
i experienced something similar, what we did was having baby in the same room with us in the mornings so she would get used to our smell and if she cries or anything we will already be there to comfort her, we also started to be more hands on, if your CN allows u can start to shower her