erjiaqing
I tested GPG, and a detached signature requires 119 bytes, which is between the 168 bytes of a full signature and the 54 bytes of a minimal signature. Furthermore, the GPG signature retains the signature timestamp and signing key information. It feels like it can fit within an area of 2.0x2.0 cm.
Additionally, have you considered alternative QR code formats, such as PDF417, which use a width-to-height ratio? This would allow the code to be placed in a corner. Alternatively, like the machine-readable area at the bottom of a passport information page, you could use fonts that are easily readable by OCR software to directly print the base45/64 content.
For example: A GPG detached signature
gpg --list-packets .\test.sig
# off=0 ctb=88 tag=2 hlen=2 plen=117
:signature packet: algo 22, keyid XXXXXXXXXXXXXXXX
version 4, created 1688418964, md5len 0, sigclass 0x00
digest algo 10, begin of digest 45 3a
hashed subpkt 33 len 21 (issuer fpr v4 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX)
hashed subpkt 2 len 4 (sig created 2023-07-03)
subpkt 16 len 8 (issuer key ID XXXXXXXXXXXXXXXX)
data: [253 bits]
data: [256 bits]
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