Set up libtmux in this repository and verify it against a real tmux server.

libtmux drives a real tmux server from code. It gives you objects for the
server, its sessions, windows and panes. Documentation for every language
is at https://libtmux.org/en/.

Language:   TypeScript
Package:    libtmux (npm)
Repository: https://github.com/libtmux/libtmux-ts

Read these before writing code:
- https://libtmux.org/en/ts/latest/llms.txt
  every page for TypeScript, as a list
- https://libtmux.org/en/ts/latest/docs.json
  the same list with headings, as JSON
- https://libtmux.org/en/ts/latest/reference/
  the TypeScript API reference
If you cannot fetch URLs, clone the repository above and read its README
and examples instead, or ask me to paste those pages in.

Set up first:
1. Report the tmux version with `tmux -V`. libtmux drives a real tmux, so
   nothing below works without one. Stop and tell me if it is missing.
2. If this directory is not a TypeScript project yet, start one:
       bun init
   Skip this in a project that already exists, and match what is here.
3. Add the dependency. libtmux has no stable release. 0.1.0-alpha.12 is the
   newest prerelease on npm, and the command below names it because the
   resolver skips prereleases otherwise.
       bun add libtmux@0.1.0-alpha.12
   Check https://www.npmjs.com/package/libtmux for a newer version, and
   prefer a stable release over this one if there now is any.
4. Write the smallest program that proves the install works: connect to a
   tmux server, create a session, confirm it is there, then kill it. Give
   that server a socket of its own rather than using the default one, so
   this never touches a tmux I am already running. Run it, and show me the
   output and the files you added.

Rules for everything below:
- Use the reference above rather than guessing names. The ten libtmux
  ports do not share spellings, and a name from another language will look
  plausible and not exist.
- If the reference does not have something you expected, say so instead of
  writing a call that does not exist.
- Follow the conventions already in this repository.