It's not that lowercase is a
problem, it's that aztec is more efficient at it.
Note that GP is incorrect that you need lowercase to express URLs and qrcode has an "alphanumeric" mode (based around uppercases which works fine), but even then qrcode's alphanumeric mode is slightly less efficient as it needs 5.5 bits per character versus 5 for Aztec.
Kanji has its own qrcode encoding mode (the qrcode encoding modes are numeric, alphanumeric[0], byte, kanji, structured append[1], ECI[2] and Code128[3]).
[0] digits, uppercase ascii letters and 9 symbols
[1] to split messages across multiple codes
[2] additional "local" encodings: https://strokescribe.com/en/ECI.html
[3] https://en.wikipedia.org/wiki/Code_128
