On MacOS, I used Automator.
I created a Service that works with Chrome, takes no input, and runs a shell script and sends the output to the clipboard. The shell script is very basic:
DateTime=`date "+%Y-%m-%d %H:%M"`
echo $DateTime
I could have done without the intermediate variable and just run the date command, but I had the idea that I might want to do extra processing and formatting. Note that if you want to include spaces in your formatting of the date string, the formatting argument must be in quotes. The screen shot uses an underbar instead.
With the script saved, I went to System Settings > Keyboard > Shortcuts, I found my script DateTime2CB.workflow in the Text section and gave it a hotkey. There's no easy way of finding out what hotkeys are in use.
I could have made it for any app (and if I find myself trying to use it other apps I still might do that), but for now it's Chrome only. I could also have had the shell script pipe the output of date to the clipboard, pbcopy on Mac, as above (using "clip"). I've tested both methods and they work.
I added the same script to another Mac and it was set up to insist that the Automator file (name.workflow) be saved in iCloud. in that context, it was not listed in the Keyboard settings. To fix that, I had to reopen the saved iCloud file in Automator using Open > Recent. It asked if I wanted to install the file in Services. A yes answer at that point saved it on my local system and I could find it under Settings > Keyboard > Shorcuts > Services.
I hope this helps other Mac users.
August