fix: doctor probes backend readiness; install.sh resolves user-scripts dir

Addresses the third review round on PR #481.

- `bot-bottle doctor` now checks `is_backend_ready()` (a full backend
  status() probe: daemon reachable, network pool present, KVM usable)
  instead of the cheap PATH-only `is_backend_available()`. A host with a
  stopped Docker daemon or half-configured Firecracker no longer reports
  `ok: backend` / exit 0 when `start` can't actually work; each not-ready
  backend prints its own diagnostics, and doctor passes only if at least
  one backend is ready.
- `install.sh` resolves the pip `--user` scripts directory from the
  interpreter (`sysconfig.get_path("scripts", get_preferred_scheme("user"))`)
  instead of hardcoding `~/.local/bin`, which is wrong on a python.org
  macOS interpreter (`~/Library/Python/<X.Y>/bin`). The PATH guidance now
  prints the actual directory.

Tests: doctor tests mock `is_backend_ready` (the readiness contract) and
cover the not-ready → fail path; a new install-script test drives the
macOS `osx_framework_user` scheme and asserts it resolves a
non-~/.local/bin directory.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

docs/prds/prd-new-install-script.md

@@ -33,7 +33,7 @@ user whether their host is actually ready to run a bottle.
   `bot-bottle doctor`. It never installs Docker or a VM backend silently
   and never uses `sudo`.
 - `install.sh` is idempotent — safe to re-run.
-- `bot-bottle doctor` reports Python version, backend availability, and
+- `bot-bottle doctor` reports Python version, backend *readiness*, and
   config-dir presence, exiting non-zero when a hard prerequisite is unmet.
 - The package keeps **zero runtime pip dependencies** (stdlib-only,
   matching the existing constraint in `AGENTS.md`).
@@ -129,8 +129,11 @@ A POSIX `sh` bootstrapper that:
 4. Installs via `pipx` if available, else `python3 -m pip install --user`.
    The spec defaults to the git URL and is overridable via
    `BOT_BOTTLE_INSTALL_SPEC` (used by tests / local installs).
-4. Locates the `bot-bottle` entry point (PATH or `~/.local/bin`).
-5. Runs `bot-bottle doctor` and reports the result.
+5. Locates the `bot-bottle` entry point: PATH first, else the
+   interpreter's own user-scheme scripts dir resolved via `sysconfig`
+   (`~/.local/bin` on Linux, `~/Library/Python/<X.Y>/bin` on a python.org
+   macOS interpreter — not hardcoded).
+6. Runs `bot-bottle doctor` and reports the result.
 
 It is idempotent and never calls `sudo`.
 
@@ -140,10 +143,12 @@ A new store-free subcommand (no DB migration required) that checks and
 reports:
 
 - **python** — interpreter version (hard requirement: ≥ 3.11).
-- **backend** — at least one backend available on this host
-  (macos-container / firecracker / docker), reusing
-  `is_backend_available()` rather than hardcoding Docker, since the
-  default backend is now a VM backend. Hard requirement.
+- **backend** — at least one backend *ready* on this host
+  (macos-container / firecracker / docker), via `is_backend_ready()` — a
+  full backend `status()` probe (daemon reachable, network pool present,
+  KVM usable), not a PATH-only check: a stopped daemon or half-configured
+  backend must not report `ok` when `start` can't work. Each not-ready
+  backend prints its own diagnostics. Hard requirement.
 - **config** — whether `~/.bot-bottle/` exists (advisory only; `start`
   provisions on first run).
 
@@ -152,7 +157,8 @@ Exits 0 when both hard requirements pass, non-zero otherwise.
 ## Testing strategy
 
 - Unit test `bot-bottle doctor` success/failure paths with backend
-  availability and Python version mocked.
+  readiness (`is_backend_ready`) and Python version mocked, including the
+  available-but-not-ready → fail case.
 - Unit test that `pyproject.toml` parses, declares the entry point and an
   empty `dependencies` list, and that every `package-data` glob resolves
   to a file that exists on disk (guards against drift).