What is Syncthing doing when it says “Scanning”, and what’s the point of it?

To answer that we first need to talk about the index database.
The Index Database

Syncthing keeps a index database with information about each file, directory, and symlink it knows about. Each entry contains the name of the item, some metadata like size, timestamps, and permissions; internal information like a version vector and sequence number, and a list of the blocks making up the file. The index is keyed on folder ID, device ID, and file name.