Full-screen for the entire application does not usually make the same assumptions as browser elements using [full-screen API] do (e.g., to remove all or some UI and allow users to watch videos or play games without distractions); the former conventionally preserves users' setup. From what I can see, neither Edge or Vivaldi alter the display of the vertical tabs in full-screen mode (I attached labeled screenshots), while Edge collapses its right-hand sidebar in the full-screen mode (which I'd argue is unexpected). What you would like to do will be possible with the expand-on-hover functionality, but it is not an expected result of the full-screen mode behavior.
Bug 1927457 Comment 3 Edit History
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Full-screen for the entire application does not usually make the same assumptions as browser elements using [full-screen API](https://developer.mozilla.org/en-US/docs/Web/API/Fullscreen_API) do (e.g., to remove all or some UI and allow users to watch videos or play games without distractions); the former conventionally preserves users' setup. From what I can see, neither Edge or Vivaldi alter the display of the vertical tabs in full-screen mode (I attached labeled screenshots), while Edge collapses its right-hand sidebar in the full-screen mode (which I'd argue is unexpected). What you would like to do will be possible with the expand-on-hover functionality, but it is not an expected result of the full-screen mode behavior.