Tailscale serve maintains a set of listeners so that serve traffic from
the local device can be properly served when running in kernel
networking mode. #10177 refactored that logic so that it could be reused
by the internal web client as well. However, in my refactoring I missed
actually calling the serve handler to handle the traffic.
Updates #10177
Signed-off-by: Will Norris <will@tailscale.com>