How do I respond to an adult child when he says that he misses the mom he had growing up and would like to see her again?

Well you probably miss her too!
We would all like to have the energy and spunk we had before so much “life” happened.
He is perhaps saying that about missing you when what he means is he is concerned about you.

How did you take what he said? How did you feel?

Perhaps he always saw you as able and willing and maybe not so much anymore.
Our moods and feelings and emotions are not light switches that can be flipped at will but we can do things to build ourselves up emotionally.
You may be running on empty and the adult child sees that but doesn’t know what to do to help?

I just recently found a guy who talks about feelings. I’ll attach his link. Listen to a few of the blogs to see if it’s helpful. I’m sorry if I’m way off on what you are asking. But I think you have to let him have his feelings and not decide it’s wrong of him or bad for him to have them (if you even did). That could be me projecting. Of course that means you get to have yours too.

https://www.marcbrackett.com/

This second one is Brene Brown. She also works with emotions. She was interviewing him on one of her blogs.

https://podcasts.google.com/?feed=aHR0cHM6Ly9mZWVkcy5tZWdhcGhvbmUuZm0vdW5sb2NraW5nLXVz

I would spend time commiserating with him and reminiscing about his mom - get out the photo albums, ask about the favourite foods she made, that kind of thing.