Unable to Transfer Club Ownership

Your admins don’t have premium membership.
They don't need one. I recently was transferred ownership of a club and never once have I gotten a membership.

I am the owner and super admin of a club that I want to transfer ownership of, but none of the super admin options appear for me, only the ability to kick out, ban, or mute other members. They are definitely premium members, so I am unsure as to the issue.
You're not actually a Super Admin of that club. That page lists owners there , regardless of club membership level. If you inherited the owner position, that can happen.
As to needing premium, basic members can create clubs now, so that shouldn't be an issue.
You'll likely have to get support to do it.
https://support.chess.com/article/346-contact-us
I am the owner and super admin of a club that I want to transfer ownership of, but none of the super admin options appear for me, only the ability to kick out, ban, or mute other members. They are definitely premium members, so I am unsure as to the issue.