No, you cannot. Docking Developer tools for the device is disabled in Blisk browser. Developer tools for the device will open in a new window.
It is caused by the width of the device content. Usually its width is from 300px to 500px wide. Therefore, there will not be enough space to work with Developer tools as you have got used to.
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Learn more about Developer Mode, Development Domain, and Device Manager on Blisk Documentation.