Bringing Astrid Tasks back from the dead
On the phone I use https://tasks.org/ to take new items or work with todos through the caldav interface (but that's android, guessing something similar exists for Apple stuff)
An implementation of Org mode without the dependency of Emacs - built for mobile and desktop browsers
For mobile I've been using organice, and synching through gitlab https://github.com/200ok-ch/organice
Appwrite - The Open Source Firebase alternative introduces iOS support . Appwrite is an open source backend server that helps you build native iOS applications much faster with realtime APIs for authentication, databases, files storage, cloud functions and much more!
Joplin - an open source note taking and to-do application with synchronisation capabilities for Windows, macOS, Linux, Android and iOS.
I don't know how complex your Taskmamagement is. But if it's simple task management (Todo list with the option to add some text to each entry on a subpage) you're after and only the synching is a problem, you could have a look at "Joplin" https://joplinapp.org It also allows you to select an external editor on your pc, if you don't like the internal one, I think.
Orgzly is a free and open source note taking and to-do app with an incredible amount of customization and multiple synchronization options
3 projects | reddit.com/r/orgmode | 23 May 2022
generating tables with babel
2 projects | reddit.com/r/orgmode | 30 Apr 2021
Org-habit mobile alternative for non-Emacs user
2 projects | reddit.com/r/emacs | 29 Mar 2021
Adding a subheading in orgzly
1 project | reddit.com/r/orgmode | 8 Aug 2022
Learning Emacs for note-taking.
1 project | reddit.com/r/emacs | 2 Aug 2022