Option One: By browser extension

For chrome and firefox
https://www.awesomescreenshot.com/
How to:
https://www.youtube.com/watch?v=dCI1wN_CXCE

Option two: By OBS software.
https://obsproject.com/

OBS Setting to reduce file size
https://www.youtube.com/watch?v=2U042cwRU8E
(Use this setting + mp4 format. This will produce around 1 hour of video in 110 MB)

OBS Studio Always minimize to system tray
https://www.youtube.com/watch?v=oz66BLw2S48

How To Set Shortcut Key For Start Stop Pause Recording in OBS Software
https://www.youtube.com/watch?v=Gki8v7ZXoOQ
(Use a shortcut key or combination of shortcut keys that doesn’t conflict with other software or applications)