The openssl docs say nothing about this issue, and no answer from the community. So I tried to figure it out with a small experiment. I created a private key (not encrypted) with:
openssl genrsa -out key.pem
Then I encrypted the key twice, using the same password:
openssl rsa -aes256 -in key.pem -out key-enc-1.pem
openssl rsa -aes256 -in key.pem -out key-enc-2.pem
and compared the content of key-enc-1.pem and key-enc-2.pem
Files were completely different so it looks like the AES-encryption is done with a random salt.
So, answering my own question: using openssl genrsa with aes-encryption, it is safe to use the same password for all my private keys.