The nanny service isn’t a regular scheduled thing like in old games. I think you call them over when you want to play as the toddlers while the parents are at work. If there are no adults on the lot, the kids are automatically sent to free daycare, so the nanny is just a way for you to keep the kids active at home with adult supervision.
So I’d have my toddlers building skills and stuff and playing and then getting the nanny to give them food or help them potty. I don’t think it’s worth doing for babies - just let them go to daycare.
When the parents come home, I usually keep the nanny around while I take care of the parents needs and the nanny can attend to the kids. Then I dismiss them until I need them again.
For gardeners, since the update gardening has been really easy - plants rarely need watering in my game because of all the rain. It’s mainly just weeds that pop up occasionally and bugs if the plants are high quality. I leave the gardener to take care of those, but my sims tend to love autonomous gardening for some reason, so I have to keep a lookout to make sure they leave stuff for the gardener to do.
Generally, a gardener is useful if you have a lot of plants hat need maintenance. If it seems like your sims are taking care of stuff OK on their own, maybe you don’t need one?