[WIP] Fix OSC8 link rendering cleanup issue

[Copilot]

Thanks for asking me to work on this. I will get started on it and keep this PR's description up to date as I form a plan and make progress.

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This section details on the original issue you should resolve

<issue_title>OSC8 Link rendering does not clean up</issue_title>
<issue_description>There is a bug in the output render with OSC8 where it's not getting cleared properly:

Originally posted by @tig in #4850 (comment)
</issue_description>

<agent_instructions>To reproduce this you'll have to add tests that use the driverassert helper that looks at the ioutput output. </agent_instructions>

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