What is the critical nature of the Kármán line boundary according to the physical reality described?

It represents a legal and physical convention, not a sharp physical border.

The Kármán line at 100 kilometers should not be perceived as a distinct physical wall or sudden cutoff point in the atmosphere. Instead, it functions as a practical, agreed-upon legal and conventional threshold established by international bodies. The Earth's atmosphere does not end abruptly; rather, it diffuses gradually over hundreds of kilometers into the vacuum of space. Because there is no single, universally accepted physical parameter—like a specific pressure reading or density value—that definitively separates 'air' from 'space,' the 100 km convention serves as the necessary, albeit somewhat arbitrary, engineering and legal demarcation line used for classifying achievements.