Otherwise, parts of the DSC will be missing - we try to make it as
complete as we can.

Since the span cannot be updated anyhow (e.g. the name cannot be
changed), we can safely freeze this at this time.

Extracted out of
#14955

…tion` (#14959)

Extracted this out of
#14955

We used to rely on implied stuff here quite a bit, which breaks if we
start returning non recording spans. Honestly this just surfaces that
this is not really ideal as it is 😬 We already pass the client around
there everywhere, so this PR updates this so we keep the active idle
span as non-enumerable prop on the client, ensuring this is consistent
and "pure".

…ns (#15108)

Extracted this out of
#14955

Instead of registering a general hook & filtering there, we can just use
the `beforeSpanEnd` hook that we already have/use to do this instead.