Sync (preferably NOT just via Nextcloud...looking at you, Saber)
Handwriting recognition is a plus, but not required
As mention above, Saber fits the criteria well, but I don't use Nextcloud and that is the only sync available in that app (unless something has changed in the last couple of weeks). I have a Galaxy phone and tablet that both support S-pen and Samsung Notes is excellent, and free, but they're not exactly privacy concious, so I'm looking elsewhere. I had considered the Excalidraw plugin for Obsidian, but I'm not sure if that works on the Android version of the app.
Yes PLEASE. I only have one more requirement: eraser button support. Without that button writing is terrible but I can't find a single app supporting it besides Samsung Notes.
The Obsidian plug-in Exaclidraw does support it with a script add on, but seemingly only supports Windows Surface pens...which is lame. Nebo is another app I'm looking at. But it can only sync with Google Drive and Dropbox. I haven't looked into the local files to see if it can manage a Syncthing type scenario between my tablet and phone yet, but I intend to. Nebo's eraser works by holding the s-pen button down and drawing over what you want gone. Not sure if that's exactly what you want. I may have to add a feature request to Saber :)
I should mention it's not a free app. But it has the best handwriting recognition I've ever seen. I write worse than a toddler and it still converts without fail to the correct text. If I can sync without using Dropbox and Drive, I'd be fine using it as Samsung Notes alternative