is F5 acting as a proxy for IP forwarding VS?

F5 LTM is described as full proxy. I understand that the following data path between my client, the F5 and the server for TCP trafficis as follow: we have 2 TCP connections where F5 ends the TCP1 connection and F5 establishes a second TCP connection (TCP2) toward the server. (as pictured below)

client--(TCP1)---F5---(tcp2)------server

This is true for a majority of virtual server types such performance L4, standars and performance HTTP.

But what about forwarding IP and forwarding L2? do we still have the path with 2 TCP connections or is the F5 acting as a simple router with the following data path: client--(TCP1)---F5---------server

thanks