Which feature only implements on the Cisco ASA in the transparent mode?

Inspecting the application layer of traffic is a capability of both transparent and routed mode ASAs, via inspection engines and application-specific policies.

Stateful inspection is a fundamental feature of the Cisco ASA, present in both transparent and routed firewall modes, allowing it to track the state of connections.

When a Cisco ASA operates in transparent firewall mode (also known as "bump in the wire"), it acts as a Layer 2 bridge. This means it can filter traffic between hosts that reside in the same IP subnet without requiring any changes to their IP configurations. In routed mode, the ASA operates as a Layer 3 router and cannot inspect traffic between hosts on the same subnet unless that traffic is routed through it.

Inspecting anycast traffic is a routing/network design consideration, not a feature exclusively tied to transparent mode; ASAs in either mode can inspect traffic that matches their security policies, including anycast if it traverses the firewall.