Someone else might have a better recommendation for a single time-tracking app with the kind of built-in recurring reminders you’re looking for, but Shortcuts could probably still work…
I do this, which might be a starting point for you.
The recurring reminder part isn’t too much of a problem (I might use Due for that part). Question is how/where you want to log what you’re doing. I’m fond of logging time direct to my calendar, but if you’re not using a specific time logging app to capture the data, you might append entries to a text file in iCloud or Drafts or some other Shortcuts enabled app that can accept text input that’s already in your toolkit.
You could schedule notifications from within Shortcuts using Toolbox Pro. The notification itself could be set to run a shortcut that prompts you to note current task/item and append that text to a file. For ease/speed, you could set this up with some default text (e.g. “continued”) to indicate that you’re continuing the same task/action from the previous 30 minute block. The final actions of that shortcut could set up the next 30 minute reminder (or not, if you’ve finished tracking for the day).
Again, as an alternative, you could use Due for the recurring reminder part, with similar thinking for logging notes/actions and setting the next timer. I’d probably trust Due to get my attention more than I’d trust a notification.