Starting nursery is a big deal! A significant change in his life, even one that doesn't seem like a big deal to us, can be stressful on a little one.
Does he like the nursery program?
Does he show any other signs of stress?
Does he have a hard time starting nursery in the mornings?
To me it sounds like he's just adjusting to the separation from you when he goes to nursery and may need some extra attention. The bedtime routine sounds great, I would keep that up. Maybe add bath time before the bedtime story, to give him some added opportunities to connect with you? You can sit next to the bathtub and talk and play and giggle. Excellent bonding opportunity! (though I see now you are already doing bathtime, you may need other 'special time' that you set aside for connecting.
After a bedtime story and lots of snuggles, I think it is appropriate to remain firm and say things like "Goodnight. I love you." and then leave. If he gets out bed, just put him back into bed with "It's bed time. Goodnight." Though it can be unbelievably frustrating, but consistently, and calmly, keep putting him back into bed with a "It's bedtime. Goodnight." Staying in the room with him will teach him the way to get your attention is by staying awake!
As long as he has been fed, watered, and loved, I don't see any major problems here, especially if you don't see any other signs of distress or discomfort.
Try asking him what's going on. "I notice you aren't sleeping. How come?" But he or may not be able to tell you much. Without knowing him it is hard to say, there's such a range at this age!
You could also make a bedtime routine chart with him. Let him do all the artwork and choose pictures to cut out from magazines to represent the different steps. Involving him can help him take ownership of the process. Give him lots of "wow, you are really learning to take care of yourself" and other reflections (not praise).
I am sure it will settle down when he gets used to going nursery. It is a big step for a little one, and some are more sensitive to changes, particularly in routines, than others.
Good luck and keep us posted on how it goes!