It can do Pomodoro sessions, but I'm adding a couple of variant timers (alarms, actually) that are designed to eventually work around your schedule:
https://radleymarx.com/2021/time-journal-wireframes-round-tw...
not trying to be negative about your idea. but the best app is one that will know automatically what's on my schedule, without me having to enter it explicitly. that way I can't forget. I have no idea how to do this, it doesn't really sound possible. Just trying to convey my experience with projects like you described
As for upkeep, I found that the app is self-motivating. It's not measuring anything so if you miss an hour or a month it doesn't matter, there's no overwhelming guilt. The only thing you miss is being able to review what you worked on.
Lots of them don't account for real life events. Having to go to the doctor, going shopping, cleaning the household, spending time with your loved ones and doing sports aren't necessarily unproductive.
Most productivity happens for me when I have an idea and am able to start working on it immediately while keeping the focus on it without external distractions... It would be amazing if a productivity app out there is able to "juggle around" all the necessities of the day while respecting external dependencies (like an appointment at the doctor) that cannot be rescheduled.