OSC 8 hyperlinks not clickable inside tmux (statusline and PR links)

Description

OSC 8 hyperlink escape sequences are not clickable when Claude Code runs inside tmux. This affects:

1. Statusline hyperlinks — Custom statusline commands that emit OSC 8 sequences render as plain text instead of clickable links
2. Claude Code's own PR links — Links displayed by Claude Code (e.g., after creating a PR with gh pr create) are not clickable in tmux

The same OSC 8 sequences work correctly:

• Outside tmux (direct terminal) — clickable
• Inside tmux when output is rendered directly (not through Claude Code) — clickable

Reproduction Steps

1. Configure tmux with set -as terminal-features ",*:hyperlinks" in .tmux.conf
2. Restart tmux (tmux kill-server + reopen)
3. Verify OSC 8 works in tmux: printf '\e]8;;https://example.com\e\\Click Me\e]8;;\e\\\n' — should be clickable
4. Run Claude Code inside tmux
5. Observe that:

• Statusline commands emitting OSC 8 sequences produce non-clickable text
• PR links and other hyperlinks shown by Claude Code are not clickable

1. Run Claude Code outside tmux — same links are clickable

Environment

• macOS 15.7.4 (Sequoia)
• tmux 3.6a with terminal-features *:hyperlinks enabled
• Ghostty (xterm-ghostty) as outer terminal

Expected Behavior

OSC 8 hyperlink sequences should be preserved and rendered as clickable links by the terminal when Claude Code runs inside tmux, just as they are outside tmux.

Actual Behavior

OSC 8 sequences appear to be stripped or not forwarded to the terminal when Claude Code renders output inside tmux. Text displays correctly but is not clickable.

Analysis

Since raw OSC 8 output produces clickable links when rendered directly in a tmux pane, the issue is likely in how Claude Code captures and re-renders output. Claude Code may be wrapping output in escape sequences (e.g., cursor positioning, screen regions) that interfere with tmux's OSC 8 forwarding.