Recommended and mentioned products
Console-based utility for migrating IMAP mailboxes.
Are there any pros/cons to using mbsync over imapsync out of curiosity? Only ask as I've seen imapsync recommended in many places. https://imapsync.lamiral.info/.
Joplin is a free, open source note taking and to-do application, which can handle a large number of notes organised into notebooks. The notes are searchable, tagged and modified either from the applications directly or from your own text editor.
For what it's worth, you can use a dedicated note taking app like Joplin and connect it to Fastmail storage via Webdav .  https://joplinapp.org/.