Earlier quoted context omitted.
It's similar to the systems administrator dilemma. Do your job well, it looks you are not doing very much, why are we paying you? Everything is on fire, it looks you are not doing your job properly, why are we paying you? I've worked with a few engineers over my career like the person you described and frankly they are worth their weight in gold, been able to bank on their output working reliably and consistently ove…
It just occurred to me a sysadmin log would be very valuable: Installed update X to prevent risk Y Wrote script to advance process Z on input A Etc...
I used to track my tasks in Jira with the thought that maybe my boss would look at it and see what I was doing. Of course he wasn't looking at it so I stopped doing it.
My log is mostly for me to provide a list of achievements to my boss whenever there's a review, or if I'm questioned about what I spend my time on.