I test the File and Media webpart in both browser and Teams client application. As a result, I reproduce the issue you descripted.
It's the designed behavior and I am afraid the option to "Open in new window" is not available in the Teams client application at present.
Meanwhile, to get this option in the Teams client application, I recommend you give suggestion in the feedback portal and help to make improvements. Many features of current products are designed and upgraded based on customers’ feedback. With requirements like this increase, the problem may well be released in the future. Thanks for your understanding and support.
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