You can try Elliptic Curve (ECC) keys which are mush smaller:
openssl genpkey -out small.pem.p8
The size of the PEM key is 119 bytes
You can also output to a raw DER form:
openssl genpkey -out small.der.p8 -algorithm ed25519 -outform DER
Now it's size is only 48 bytes. And it contains internally it's public key.