[idea] Command to clear pane screen and scrollback without restarting the process

[BABA983]

idea / problem

A Node.js service logging to stdout piles output into the pane scrollback. There's no way to clear it while the process keeps running. pane send-text and send-keys write to the PTY, so escape sequences echo back as literal text (^[c). They never reach herdr's terminal emulator as a control sequence.

tmux has clear-history for this. It operates on tmux's own scrollback, not through the PTY. herdr wraps ghostty_terminal_reset() in libghostty-vt, but never calls it. The reset already exists in the vendored code, it's just not exposed.

requested change

Add a socket API method and CLI command:

herdr pane clear <pane_id>

Call ghostty_terminal_reset() on the pane's terminal. This clears screen and scrollback, preserves dimensions, leaves the PTY and process untouched. Herdr already honors CSI 3 J from the pane's output. This is a separate explicit trigger, not a change to clear behavior.

why you want this

Dev servers and log-heavy processes fill scrollback over time. Users either close the pane (killing the process) or scroll through thousands of lines. A pane clear command lets a keybinding or script trigger it in one keystroke.

Related: #676 asked for the same thing with ctrl+k (closed without PR). #2897 asked for the opposite, preserving scrollback on clear.