Barrier is the solution I use to go between 2 desktops and a laptop, including mouse and keyboard control
I use an NFS share to transfer files and keep work in one central location, but a true copy-paste store across devices would be interesting. You'd have to be able to sync the clipboards across many devices, so to I'd either propogate updates in a similar way to routing protocol daemons, or go with the less flexible but easier to set up clipboard daemon->ssh-and-xclip. It would probably be wise to use a VPN like wireguard to maintain some level of security and confidentiality.
I send myself a message on whatever app I have logged in on both machines. Discord functions as a sort of notebook for me, it's quick to open on phone and I've usually got it running on laptop.
Mac’s have this already - you can even copy and paste between your iPhone and computer. It’s a feature that not many people know about. I only discovered it by accident.
One way if you seldom do it: Compose new email in gmail and it appears in the draft. Go to the other computer and you see it.
There are already services that do this. I use PastePal and it works fine.