I have no idea on the internet core, but I wouldn't be surprised if SDN capable gear is used there. One major performance benefits of SDN is lowering latency as the processing is happening in the switch silicon instead of a general purpose CPU, which seems very applicable to core switching.

For access networks, it has been used. VOLTHA (PON solution that is in production in various places, see other post) is being used for this, and also there is code for doing PPP encap/decap in P4, which allows access control and lower latency at line rate.

I'm not aware of anyone making the programmability parts of SDN available as a service. Usually most hyperscalers don't allow access to infra components - anything below the kernel or certain specific peripherals - and the underlying network would be one of these areas.