get virtual servers with no traffic in the last year

There is no easy way to do this.  The problem that it needs to be done over time and with knowledge of the application and it's usage.   Some apps only get used occasionally, like yearly benefits elections or for producing tax forms.

My general recommendation is to use something like Telemetry Streaming to send virtual server usage statistics to a central dashboard where they can be viewed over time.

The BIG-IP will only keep connection stats for the last 30 days, but one must also consider last reboot and/or failover time