Why isn’t BetterDisplay available in the Mac App Store?
BetterDisplay uses private or undocumented macOS interfaces for some of its display features. Those interfaces are incompatible with the Mac App Store’s requirement to use public APIs, so the app is distributed directly.
Download BetterDisplay through the official website. App Store availability is separate from whether a particular download can open successfully. A launch error needs its own diagnosis.
Additional sources
Apple’s App Review Guidelines, section 2.5.1 describe the public-API requirement.