Since they don't have authority over what other states do or what other state's licenses show, this should only be relevant to KS licenses and KS government records. At least I haven't heard or read anything indicating otherwise.
BUT another thing to be aware of is that this bill also bans anyone from using a bathroom marked as for other than one's gender assigned at birth. IMO this is just as bad if not worse. I expect bad things to happen because there are always those people out there who want to make bad things happen.
I was actually surprised to learn that the bill was going to invalidate documents because it was always called "the bathroom bill" and all I ever read or heard about it was about the bathroom aspect of it. I don't think I ever once heard anything about driver's licenses and birth certificates being invalidated.
It's all about taking away trans rights and women's rights and implementing christian nationalism.