Updates are not offered when running macOS with the -no_compat_check boot arg. There are 2 x pre-requisites for obtaining Big Sur update offers:
the SMBIOS of a Mac model compatible/supported by Big Sur (MBP11,x minimum).
a SIP value that does not enable Apple Internal; it's disabled by default and must be kept disabled (bit #5 of SIP value, see here for details).