What is the What's New limit?
4,000 characters. App Store Connect Help says What's New is limited to 4000 characters.
Do you need What's New for your first version?
No. It isn't available for an app's first version, and it's required for every version after that.
What does Apple require in What's New?
App Review Guideline 2.3.12 says apps must clearly describe new features and product changes. Simple bug fixes, security updates and performance improvements may use a generic line, but significant changes have to be listed.
So "Bug fixes and improvements" is fine for a small release, and not for one that adds a feature.
Where else can you say what's new?
What's New changes only with a version. To tell people about something between releases, such as a sale or an upcoming feature, use promotional text, which you can change any time.