Whatever's under your connected address in the indexer's ledger — same data as the Holders list on the mint page, just filtered to you.
Nothing under this address yet —
mint one, or it just hasn't been indexed yet (~5 min after payment confirms).
Transfer — Soon. Sending a cat to another address isn't wired up yet.
Offers — Soon. No marketplace/bidding yet — mint-only for now.
Activity — Soon. A per-address mint/transfer history isn't built yet.