Referenced in microsoft/vscode-python#5662 were two good ideas for adding execution time to each cell:
First idea -
The extension for Jupyter solves it like this: jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/execute_time/readme.html. A single line with a timestamp and the execution time in milliseconds below every executed cell.
But I guess that would not look as pretty in vscode as it would clutter the window. Maybe the execution time could be displayed on hover: Either over the cell or over a designated area like a button? The execution time could also be displayed in the status bar at the very bottom. Or maybe the execution time is displayed after clicking a button, like you suggested? Or maybe there could be a button at the very top, that globally enables and disables the display of the execution time below each cell.
Second idea -
How about adding a little info icon to every cell by default next to the "Remove cell" and "Go to code" buttons which on hover displays the cells execution time and when it started running. Something like this.

The cell Execute Time would be a really useful feature. Once you get used to it in a Jupyter Notebook (through this extension) it's really difficult to move to JupyterLab or VS Code notebooks without this important functionality. Hope it gets added to VS Code as an option.
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The cell Execute Time would be a really useful feature. Once you get used to it in a Jupyter Notebook (through this extension) it's really difficult to move to JupyterLab or VS Code notebooks without this important functionality. Hope it gets added to VS Code as an option.