thanks for your question. Unfortunately this is currently not possible.
The currently selected time range is stored in Javascript memory and in the url in the ?_g= part of the hash. If you are doing a navigation in the same window, Kibana is able to restore the time range from Javascript memory. If you are opening a new tab though, the Kibana web app is started again from scratch and only has the hash URL parameter in the URL as a source - which is specified in the markdown vis itself and does not include the current ?_g= part of the hash because it's statically defined. That's why Kibana in the new tab falls back to the default time or dashboard time.
I totally see your use case - if you want to feel free to create a feature request in the Kibana Github repository.
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