Sinatra instrumentation throws errors when using multiple Sinatra app classes

Description of the bug

If you build a Sinatra app that uses other Sinatra apps as middleware (a documented pattern for dividing endpoints into multiple classes), the default OpenTelemetry instrumentation throws errors every time an endpoint is called.

See "Using Sinatra as Middleware" here: https://sinatrarb.com/intro.html

Share details about your runtime

Operating system details: MacOS, Tahoe 26.5.1
RUBY_ENGINE: "ruby"
RUBY_VERSION: "3.3.4"
RUBY_DESCRIPTION: "ruby 3.3.4 (2024-07-09 revision be1089c8ec) [arm64-darwin23]"

Share a simplified reproduction if possible

MCVE here: https://github.com/isaaclyman/opentelemetry-instrumentation-sinatra-detach-error-mcve

• Install Sinatra and OpenTelemetry
• Set up the OpenTelemetry SDK with use_all
• Create two classes that inherit from Sinatra::Base, as described in "Using Sinatra as Middleware"
• Add a basic endpoint to the first class
• Have the second class use the first one
• Send a request to the endpoint

You see the following in the application console:

W, [...] WARN -- : Calling finish on an ended Span.
E, [...] ERROR -- : OpenTelemetry error: calls to detach should match corresponding calls to attach.

Additionally, the generated trace has a missing parent span.

The problem disappears if you have only one class that inherits from Sinatra::Base and don't use any other classes as middleware.

It also disappears if you pass install_rack: false as an option to OpenTelemetry::Instrumentation::Sinatra, but then traces are not produced.

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