This fixes two things. First, it better tracks the calling context and the
target context, so that if a parent frame does a document.write within a child
frame, any JavaScript is executed in the child frame's context (previously, it
would be executed in the parent's context).
Second, it ensures that, on document.write, we force-execute any pending
scripts. This is related to https://github.com/lightpanda-io/browser/pull/2542
but applies specifically to document.write.
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