This BIG-IP system has encountered a configuration problem that may prevent the Configuration utility from functioning properly

There problem seems to be here:

net stp /Common/cist { 
    interfaces {
        1.0 {
            external-path-cost 200000
            internal-path-cost 200000
        }
        1.1 {
            external-path-cost 2000
            internal-path-cost 2000
        }
        1.2 {
            external-path-cost 2000
            internal-path-cost 2000
        }
    }
    vlans {
        /Common/external
        /Common/internal
    }
}
net vlan /Common/external {
    interfaces {
        1.2 {}
    }
    tag 4093
}
net vlan /Common/internal {
    interfaces {
        1.1 {}
    }
    mtu 9001 tag 4094
}

You can try and remove the following:

    1.0 {
        external-path-cost 200000
        internal-path-cost 200000
    }

and see if it gets loaded:

 tmsh run /sys config load

No harm in trying but back up the conf file somewhere else first before you do this.