Hello S. Miwa,
MIFARE Ultralight does not provide a command to write 16-bytes at once.
The COMPATIBILITY_WRITE command is used to ease the compatibility with systems initially designed for MIFARE Classic, as it matches the MIFARE Write (A0) command framing, but from the 16 bytes only the first 4 bytes are written and the rest are ignored as you have seen already.
I hope this clarifies.
Best Regards!,
Jorge Gonzalez
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