You failed to provide the content of ./sign-file so we don’t know what that script actually does.
Also. it seems you put the keys into the kernel subdir that is specific to that kernel which requires the keys be either copied over each time a kernel is updated and a new module generated or a new signature needs to be generated each time the kernel is updated.
As you can tell from the first post in Installing nvidia drivers on a fedora 36 (in dual boot with windows 11) with secure boot enabled the kmodgenca command creates a public key file at /etc/pki/akmods/certs/public_key.der
(the post tells how to generate the key and to install it to bios)
If you were to generate your key in this way the same key could be used for both manually signing the module the way you do and for using it with akmod packages that build the module with akmods. It would only require modifying the path to the keys.
Generating one key is all that is required with the public key at /etc/pki/akmods/certs/public_key.der and the private key at /etc/pki/akmods/private/private_key.der