Switch to OpenTracing's `ContextVarsScopeManager` instead of our own
custom `LogContextScopeManager`.
This is now possible because the linked Twisted issue from the comment
in our custom `LogContextScopeManager` is resolved:
https://twistedmatrix.com/trac/ticket/10301
This PR is spawning from exploring different possibilities to solve the
`scope` loss problem I was encountering in
https://github.com/element-hq/synapse/pull/18804#discussion_r2268254424.
This appears to solve the problem and I've added the additional test
from there to this PR ✅