docs: remove obsolete Claude Code and omp docs, update references

docs/shell/bash-zsh.mdx

@@ -76,6 +76,7 @@ The tv pickers have their own widgets, because `tv --inline` opens on the line b
 | <kbd>ctrl-t</kbd> | tv smart autocomplete (from `tv init zsh`) |
 | <kbd>down</kbd> | `pj-down`: `PJ_QUIET=1 pj` on an empty prompt, otherwise `down-line-or-history` (bound to `^[[B` and `^[OB`) |
 | <kbd>ctrl-a</kbd> | `omp-session`: resume or start omp for the current repo ([Scripts](/shell/scripts#omp-session)) |
+| <kbd>ctrl-n</kbd> | `omp`: always a new omp session (replaces zsh's `down-line-or-history` on that key; <kbd>down</kbd> still walks history) |
 | <kbd>ctrl-g</kbd> | `lazygit` |
 | <kbd>ctrl-q</kbd> | `exit` |
 | <kbd>ctrl-c</kbd> | At the prompt: kill the buffer, clear the screen and kitty scrollback (`ESC[2J ESC[3J`), reset the prompt |

docs/shell/fish.mdx

@@ -186,6 +186,7 @@ The header comment says the file should stay empty, but it holds the following:
 | <kbd>ctrl-o</kbd> | `_gho_bind`: `gho` (pick a ghq repo or Obsidian vault from the `ghq-repos` cable and cd into it), then repaint |
 | <kbd>ctrl-p</kbd> | `_pj_bind`: `pj`, the task runner on the `pj` cable ([Scripts](/shell/scripts#pj)), then repaint |
 | <kbd>ctrl-a</kbd> | `omp-session`, then repaint: resume or start omp for the current repo by branch and session age, opening the `omp-sessions` cable only when nothing qualifies ([Scripts](/shell/scripts#omp-session)) |
+| <kbd>ctrl-n</kbd> | `omp`, then repaint: always a new omp session |
 | <kbd>ctrl-w</kbd> | `atuin ai inline`: natural-language command overlay |
 | <kbd>ctrl-z</kbd> | `_jobs_bind`: with one background job, `fg` it; with several, pick one from the `jobs` cable ([television](/tools/television#jobs)) and `fg` that; with none, nothing. While a job holds the terminal, ctrl-z is still the tty's suspend, so the key toggles suspend and resume |
 | <kbd>ctrl-g</kbd> | `lazygit` |

docs/shell/scripts.mdx

@@ -247,7 +247,7 @@ Reads lines on stdin and prints them newest-first by the mtime of each line's la
 omp-session
 ```
 
-Starts or resumes [omp](/ai/omp) for the current git repo by fixed rules, so <kbd>ctrl-a</kbd> never asks when the answer is obvious.
+Starts or resumes omp for the current git repo by fixed rules, so <kbd>ctrl-a</kbd> never asks when the answer is obvious.
 
 | HEAD | Does |
 | --- | --- |
@@ -256,7 +256,7 @@ Starts or resumes [omp](/ai/omp) for the current git repo by fixed rules, so <kb
 | Detached | Opens the `omp-sessions` cable (a new session when there are none) |
 | Outside a git repo | Plain `omp` |
 
-Resuming runs `omp --resume <session file>`; omp switches to the session's own cwd.
+Resuming runs `omp --resume <session file>`; omp switches to the session's own cwd. `omp-session --new` runs plain `omp`; it is the cable's <kbd>ctrl-n</kbd> action and marks `OMP_SESSION_STATE` like a resume does, so the prompt is not moved after a new session.
 
 **Sessions.** Every `*/*.jsonl` under `$PI_CODING_AGENT_DIR/sessions` (default `~/.omp/agent/sessions`) whose `session` header `cwd` is the worktree root or below it, excluding worktrees nested inside it. Session age is the file's mtime (the last write).
 
@@ -272,7 +272,7 @@ Resuming runs `omp --resume <session file>`; omp switches to the session's own c
 
 **Prompt redraw.** The launcher runs `tv omp-sessions --inline` with `OMP_SESSION_STATE` set to a temp file. When the picker is cancelled (no `ran`), it prints `\033[A` to `/dev/tty` so the shell redraws the prompt in place; the key bindings just repaint.
 
-**Launched by:** <kbd>ctrl-a</kbd> in fish and zsh.
+**Launched by:** <kbd>ctrl-a</kbd> in fish and zsh. <kbd>ctrl-n</kbd> at the prompt runs `omp` directly, not this script.
 
 **Needs:** `python3`, `git`, `omp`, `tv`.