`GPR_BACKWARDS_COMPATIBILITY_MODE` was devised to support old Linux kernel with old glibc but gRPC is now expected to support glibc 2.17 and later (2.17 is derived from the oldest but supported Linux distro, CentOS 7). Effectively, gRPC doesn't need `GPR_BACKWARDS_COMPATIBILITY_MODE` anymore. Hence, let's remove it.
gRPC Python and Ruby that distribute binary artifacts already began to use `manylinux` environment dealing with this issue in a better way so they don't need this flag anymore.
Closes#35602
PiperOrigin-RevId: 599895270