For time management, there’s the Pomodoro technique where you basically break your work time into small sessions of 20~30 minutes where you work on just one thing at a time separated by short 5 minutes breaks. If you vibe with this approach, on Android there’s the Goodtime app. It’s FOSS and you can find it on F-Droid.

I also maintain to-do lists using the Quillpad app, also on F-Droid. You can also take Markdown notes with it.

For my work emails they’re obviously in our work computers and you can’t access them outside our intranet, so not accessible on my Android phone, but I still mark important meetings on my phone’s Google Calendar as I pay attention to my phone much more than my work PC’s Outlook calendar.

Also not sure if we can count this as a productivity app, but whenever I’m under too much stress there’s also the app Smiling Mind I turn to for some meditation and breathing exercises.

Finally, for all these things I find that a phone stand is also very useful. I’m using Tonyhoney (you can find it on Amazon, it’s very cheap, or someone well-versed in these things can 3D-print something similar) and it does its job very well (though not very practical if you want to charge your phone).