yes it works only with light mode... Interesting. This is something that Samsung should fix or at least make clear in the app.
I had the same problem. I initially had the dark mode and then I switched it to light mode and....nothing happened. So I then restarted my tablet ( I have tab 8 plus and note20 ultra) and then I updated my phone to latest update. I disconnected my Bluetooth connection from both devices and then I reconnected . I don't know if this matters but I disconnected my wifi connection from my tablet. I used instead my phones Hotspot connection to my tablet. So now my tablet is connected to phone by Bluetooth and Hotspot. No wifi on tablet just Hotspot from phone. I then opened the Samsung notes and opened a new note. And nothing happened , I didn't see the icon that enabled your phone to be used as tool bar but then.....after 5minutes of not touching the new note it happened! The icon appeared, that icon appeared, YES!!!! In light mode of course. I hope these steps work for you.