Syncing my clipboard between macOS and remote terminals

As I've been spending more and more time with agentic development, it's more and more important to me that sessions run somewhere other than my laptop. For the last few months, that has meant running my coding agents in tmux on either a remote Mac or a remote Linux server. The most frustrating thing for me has been that the clipboard or paste buffer on those remote hosts isn't synced to my desktop. So, if I copy something inside of a coding agent, I've had to play games to get it to my local Mac. Similarly, if I wanted to paste a screenshot to a remote tmux session. I was playing games with scp. But also, I don't just want to be able to copy and paste between my Mac and a remote terminal. I want to be able to copy and paste between remote terminals on two different computers. And I want to be able to take a screenshot on my phone and have it end up in the paste buffer on a remote Linux box. I took a run at solving this problem maybe three months ago, and I came at it from the wrong…