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.
My Note 4 died last year so I don't have any android suggestions, sorry. On Linux I like Rnote, but it's fairly early in development and I last time I wanted to annotate a PDF I had to do so in Xournal++
Agreed, I'm on a Note10+ and I love that feature. I'd setting for being able to add 3rd party app shortcuts to the little side bar thing....not sure what that's called, but it pops up when you pull the S Pen out. That wouldn't replace the screen off function, but would be a step in the right direction.
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 :)