If I update my iOS version will my iPhone storage also increase?

No. The physical storage is fixed. There might be some differences in terms of how more storage is used by the iOS installation, but that generally goes up with newer versions.

I understand that you are wondering whether moving to iOS 15 from iOS 13 will cause increased use of available storage space. The answer is that the available free storage space should remain the same or very close to where it currently is.

Axel F.