Log start/end times of when I am using my Mac

I'm required to keep a log of the hours I spend working on my Mac, for tax reasons. It doesn't need to be completely accurate - so it's fine to assume that I'm working whenever there's user input, which times out after some period of inactivity. Basically like how a screen saver works. Is there a (free) MacOS app or tool I can use to log user input to a file this way? All I need is something like:

2025/04/28 08:53:17 start
2025/04/28 12:03:20 timeout
2025/04/28 12:46:04 start
2025/04/28 14:18:20 timeout
2025/04/28 14:23:10 start
2025/04/28 17:20:55 timeout

Or, if there's an easy way to query the current state (activity or not) from the OS, I can write e.g. a bash script which runs every minute or so and does the logging itself. Thanks!