Does she have any actual toddler experience?

Because toddlers need a specific type of interaction.

Yes handling an infant + a toddler can be a bit challenging but it is doable.

Unless your toddler is getting into shenanigans in the park it's fine for him to explore on their own. But if the baby is sleeping maybe you can have her offer to push toddler on the swings or something. If the toddler is awake when the baby is asleep suggest she do crafts with them.

We have a new nanny after our previous nanny went to school (she was with my eldest for two years). Our new nanny had previous baby experience, and I think she does a great job with the baby. She is however having a harder time with the toddler, specifically when she needs to manage both, which I get is tricky! She tends to prioritize the baby and leave the toddler to be more independent than I’d like (eg., keeping an eye on toddler from afar in park for extended periods of time while manning the stroller).

I am trying direct feedback but open to other suggestions for how I can best guide her, thanks.