It's not a problem if Minio is bundled into the self hosted stack as long as it's officially supported (paying for support is also okay).
Depends on whether AGPLv3 works for you or not (or whether you decide to pay them), I guess: https://min.io/pricing
I've actually been looking for more open alternatives, but haven't found much.
Zenko CloudServer seemed to be somewhat promising, but doesn't seem to be managed very actively: https://github.com/scality/cloudserver/issues/4986 (their Docker images on DockerHub were last updated 10 months ago, which is what the homepage links to; blog doesn't seem active since 2019, forums don't have much going on, despite some action on GitHub still)
There was also Garage, but that one is also AGPLv3: https://garagehq.deuxfleurs.fr/
The closest I got was discovering that SeaweedFS has an S3 compatible mode: https://github.com/seaweedfs/seaweedfs
The org I work for would love to self-host on-premise a digital signing solution so they definitely won't use external dependencies like AWS. Theoretically they could swap with minio but last time we used it it was not a drop-in replacement yet.