Springer’s book-chapter sharing policies
This is the answer I got from Springer for a smiliar question:

"Thank you for getting in touch. Springer doesn’t have a green OA policy at this time. Chapter authors would need to choose the gold OA route. We are able to offer gold OA for chapters already published (retrospective OA) in cases where the authors need to fulfill a funder OA mandate.

Our policies regarding OA books can be found here: https://www.springernature.com/gp/open-research/policies/book-policies 

Please feel free to be in touch if you have further questions—I’m happy to help."