The details for Context management (i.e. setting current span) are
already handled by the OTel ActiveSupport instrumentation. Reuse
the notifications subscriber here for ActiveModel serialization events.

Reworked the example app into two: one Rails which works with the usual
SDK configuration and one standalone (no Rails) to demonstrate that the
subscription needs to be made after the SDK configuration is complete.
If the subscription is created during instrumentation install, the
subscription's tracer will be a NO-OP API tracer and won't produce
spans.