This isn't open source (but free if I recall correctly- I think I have a paid version but I installed it years ago): Recurlog will absolutely fit the bill for medications or other recurring tasks that repeat based on last-done date or due date (with or without automatic rollover = will reschedule for next day if one is missed).

You can set reminders at a specific time, and easily log directly from the reminder notification. You can log multiple times each day if you like, and add notes to the logged entry.

You can either set a "simple" recurring task without extra data, or optionally add data fields for text, numbers, Yes/No buttons or a time duration.

Manual backup to file. Unfortunately no encryption or visualizations.

I use it to log medications, reminders for physical exercises, cutting the dog's nails, when the dog is due to come in heat and how long it lasted, monthly hair dye and products and results etc.

I know it's old (last updated in 2018), but it's phenomenal. I've been thinking of making a similar app with more features as a hobby project, but I also have a 10 mo baby so 🤷🏻‍♀️