as a Podman developer I'd like to push layers compressed in a different format than gzip, such as zstd.

docker.io seems to support these images and I am currently using it to host some images compressed using zstd: docker.io/gscrivano/zstd-chunked, I'd like to switch to quay.io as soon as it supports zstd.

Support for zstd in the OCI image specs is under discussion yet: https://github.com/opencontainers/image-spec/issues/803

We are experimenting with zstd to support partial fetch of images:
https://github.com/containers/storage/pull/775
https://github.com/containers/image/pull/1084
https://github.com/containers/skopeo/pull/1111

For such feature to work, it is important that there is no recompression happening on the registry (i.e. the original compressed blob must be retrievable unchanged) since some metadata is embedded as part of the compression format itself.