iRule that checks client IP and send to a pool.

Try this:

when HTTP_REQUEST {
    switch [HTTP::host] {
        "testwebsiteadminservice.tcbna.net" -
        "10.144.112.71" {
            if { [class match [IP::client_addr] equals Mulesoft_Non-Prod_VPC] } {
                pool DA7POLBACORE-TEST-Pool-1135-OLB-CONE_8444
            }
        }
        default {
            reject
        }
    }
}

Also, if the source addresses are in a single contiguous subnet, you could actually just define this subnet in the Source Address field of the VIP.