Is this technology used in the Internet core?
Or for de-bundling access networks and Internet service? Where I live, access networks use shared media (broadcast cable or GPON), segregating customers through device and protocol obscurity (no tcpdump) and maybe encryption (but without tcpdump, it is hard to tell). There's not much room for defining anything in software there.
And in data centers, how far does multi-tenancy go in practice? Can tenants push their own P4 programs into hyperscaler infrastructure?
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.