Issue description

Here's a quote and video to demo the working feature straight from Ghostty which sums up the expected behavior:

Ghostty 1.3.0 now supports the click-events and cl=line extensions to the OSC 133 Semantic Prompts specification. This lets you click your mouse within an active shell prompt to move the cursor, like a normal text field.

On my machine this feature works great when I perform these steps without tmux:

• Open Ghostty
• zsh is being used
• The feature works where I can type "hello world" into a prompt and mouse click between the words to move the cursor
  • The mouse cursor turns into the I style cursor right away

It fails when I introduce tmux into the mix:

• Open Ghostty
• start tmux
• zsh is being used
• The feature doesn't work, clicking the mouse has no effect
  • The mouse cursor stays as the usual pointer cursor

I'm able to reproduce the problem using bash too, both the success and failure case.

I opened a discussion on Ghostty here ghostty-org/ghostty#11433, described the problem and the creator of Ghostty said it's likely due to tmux "messing with OSC1033" and "it's tmux's problem to fix". He mentioned these quotes in this comment.

Couple of asides:

• I have mouse mode enabled in tmux
• I use the mouse for a number of things in tmux (copying text with tmux-yank), it was never a problem
• I run Neovim inside of tmux and it supports being able to move the cursor with mouse clicks

I hope the above 3 things at least demonstrates that tmux is able to receive and pass through mouse behavior.

Required information

• tmux version: 3.6a
• Platform: Arch Linux
• Terminal in use: Ghostty
• $TERM inside: screen-256color
• $TERM outside: xterm-ghostty (setting this inside of tmux made no difference for this bug report's issue)

The logs are pretty big, I ran tmux for a few seconds, repeated the repeatable steps and attached them here.

tmux-client-101209.log
tmux-out-101211.log
tmux-server-101211.log

P.S., I'm able to reproduce this on macOS too with the same dotfiles (zsh, tmux, Ghostty configs).