This article reads like someone stumbled onto something they liked, then reasoned backwards to why everyone should use it.
Like all productivity things - if it works for you, great. But maybe don't assume your thing is the magic thing that will fix everyone else's problems just like it might have your own. Likewise, there's a pretty big difference between something that feels productive and something that is productive - something that constantly grates the back of my brain whenever I look at some of these over-elaborate bullet journal examples.
The other thing to remember is that these systems change over time. I'm a productivity nerd - I constantly change what I do and what works for me, because at different times in my life (say every ~2 years) I stumble across a system that works better for the next period. There is no magic bullet.
Not parent, but I can chime in with my current system: Simple logs that I can search and copy.
The key for me is that it's not about the format. The format changes with the context: I have a different logging strategy for fitness(Fitnotes app, and since I was just gifted one this past week, a Fitbit) from the logging used for programming notes(repetitive short block comments with date, time, and sometimes title). I have a generic diary text file that contains catch-all musings, but I am increasingly using different logs for different tasks since I don't currently face a lot of time contention that would necessitate a detailed calendar.
My logs are not just what happened but also what I wanted to happen on that date. I'll often copy-paste the same to-do list when I didn't finish it that day, or "redraft" the same thought an hour after I first logged it, with some elaborations. Keeping it around, I learn what is or isn't working at a glance by skimming over these repeats hours to months later.
Having the date and time is essential to this because it makes the log a progression: my recent activity is my most important, most of the time, and so in the case of the programming logs, I can gradually edit and eliminate them as the code changes and the momentary thoughts of "I need to do this next" grow irrelevant, while if it's something like a log of weight/reps/sets, I just want to copy, increment the numbers a little higher, and add a note about anything weird that day that may have made me change plans.
When I really need freeform notes I will turn to paper, and I can see bullet journaling techniques being worth trying in the future for adding some structure to those. As long as I have dates I can usually recreate the context of any particular note, though.
Something I just thought of: is there a browser extension that would automate logging my history when I want to research something? That's a pretty common task that I currently address manually with a lot of right clicks and ctrl+C's.
I use Trello to stay on task, easy to manage daily to-do lists while being able to just push everything to the next day and also managing long-term lists. It lets you comment, add files or links, create internal check-lists for each card, has the option for due dates, even integrations for stuff like Slack. It's great for keeping track of stuff in general. Plus it has a really friendly UI and it's free for the base package.
Asana is what we used at my last company and it's pretty much the same (at least from what I remember) with a different UI.
Another neat productivity thing I use is the Sketchpad app in the Windows Ink Workspace. My laptop has a touch screen that works with an active stylus. The app basically turns my laptop into a whiteboard on the fly (really handy for when I need to work out some complex math) and I can save a snapshot to then stick into Trello or wherever. Only gripe - Microsoft should add two-finger drag support (like in art programs like Krita) so you're not limited by you monitor size when using it.
Like all productivity things - if it works for you, great. But maybe don't assume your thing is the magic thing that will fix everyone else's problems just like it might have your own. Likewise, there's a pretty big difference between something that feels productive and something that is productive - something that constantly grates the back of my brain whenever I look at some of these over-elaborate bullet journal examples.