FCW is a visual alert and a loud warning tone to let you know that AEB may be engaged if you don't brake. If you don't do anything, AEB can engage which won't prevent the collision, just help mitigate it.
What you're experiencing is AutoPilot (AP) behavior. Unfortunately, AP code is a little long in the tooth, and the new FSD Beta code, which has replaced the older AP code, handles cut-ins and cut-outs much more smoothly.
At this point, you can either subscribe to FSD so that you can get on FSD Beta, or accept the behavior for now and wait until Tesla replaces the older AP code with FSD Beta code for freeway/highway use. We don't know when that will happen.