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 **bleep** icon appeared, that SOB icon appeared, YES!!!! In light mode of course. I hope these steps work for you.