samsung notes on other android devices

I don't think you can put most samsung specific apps on non samsung phones

The sync thing is part of samsung phones. So if you could force install it, no sync

Samsung Notes is locked to Galaxy devices and is not officially supported or able to sync via Samsung Cloud on non-Samsung phones like your Nothing Phone.

According to Google, you can access your notes on your phone by syncing Samsung Notes to Microsoft OneNote.

Samsung Notes is unfortunately designed primarily for Galaxy devices, so installing the official app on a Nothing Phone may not give you the full functionality or Samsung account sync you’re used to. Some unofficial APK methods exist, but compatibility can be unreliable and I’d be cautious about downloading modified APKs.

Since you already have years of notes, PDFs, and books stored there, I’d recommend first checking whether you can export your important Samsung Notes files to PDF or another supported format from a Samsung device, then move them to a cross-platform notes app. That way you won’t risk losing access to your existing content.