I recently stumbled upon Tasks.org which allows me to sync the tasks on my eM Client smoothly to Tasks.org on my Android.
eM Client doesn’t currently support External Third party Notes or Tasks via eg: Plugins to sync.
So if you are wanting Notes and Tasks to sync with eM Client for desktop and droid mobile, then your account in eM Client “has to normally be integrated with the tasks and notes”.
So as you are removing Google & Microsoft accounts, then you could maybe move to another mail server who does have Notes and Tasks integrated such as eg: “Imageway” as per the following eM Client page.
Quote Extract from the above page.
" Easily connect to your Imageway account using eM Client. eM Client will smoothly synchronize your Imageway emails, calendars, tasks, contacts and notes."
eM Client also has an updated mobile app coming soon which will also support Calendar, Contacts, Tasks, & Notes.
Lastly if you just want a good “separate notes app” then eg: Evernote is a good mobile app.