I just tested this out. PRAGMA data_version uses a shared counter that any connection can use while the C API appears to use a per-connection counter that does not see other connections' commits.
Reporting back. This appears to be a bug in my original test the code of which sadly I did not commit anywhere. I went back to regenerate these tests and proved the opposite - the C API is better than PRAGMA and works across connections. I am going to make that update as I've proved across dozens of versions of SQLite that this is not in fact the case.
Reporting back again. It seems I was actually right the first time - the C API's SQLITE_FCNTL_DATA_VERSION doesn't work cross connection. It is cached on each read - but if there aren't any reads (i.e. just polling SQLITE_FCNTL_DATA_VERSION) then it doesn't work.
PRAGMA data_version is pretty fast (1500ns with prepared statement) and doesn't have that issue.
Checking the wal-index is sub-nanosecond when mmapped but has slightly different behavior on Windows.
Here's the link to the thread on this, my scripts are all there.