Rewire check_installation tests onto resolve_lemonade/get_installed_version
(AC1/AC2), and pin the corrected _ensure_server_running behavior where
auto-start is attempted before the interactive "Please start Lemonade
Server" prompt in both CI and interactive modes, with a fail-fast
guarantee that a failed auto-start never hangs on input() (AC5/AC6).

Also extend the #839 ctx-size regression guard to cover the modern
LEMONADE_CTX_SIZE env-var path alongside the existing legacy --ctx-size
argv path, so a future change can't silently drop ctx-size propagation
for modern tooling while the legacy assertions keep passing.

3 pre-existing test failures unrelated to this change (already broken
on main, not introduced here):
TestEnsureLemonadeInstalledSkipsWhenPresent::test_older_version_below_minimum_triggers_install_in_ci,
TestLegacyFallback::test_not_installed_on_linux_proceeds_to_install_via_ppa,
TestLegacyFallback::test_not_installed_on_windows_proceeds_to_download_and_install

Pin that launch_server() builds its Popen argv/env from
resolve_lemonade()/build_start_command() instead of the hardcoded
["lemonade-server", "serve"] literal, with a byte-identical regression
guard for the legacy argv shape and a guard that kill_process_on_port
is skipped when health_check() already reports the server healthy at
entry.

Pin at the Popen call sites that spec.env is MERGED into the parent
environment ({**os.environ, **spec.env}) rather than replacing it — an
implementation passing env=spec.env alone would drop PATH/LOCALAPPDATA
and break LemonadeServer.exe while still passing the previous
assertions. Sentinel env var seeded before the call and asserted
retained, alongside PATH, in the three modern-path launch tests.

Also add the direct build_start_command-level Windows-legacy test
asserting --no-tray in argv, pin platform in the non-Windows legacy
test for cross-platform determinism, and replace a no-op tuple
assertion with a real assertTrue.

Modern Lemonade (10.7/10.8) removed the lemonade-server CLI; the server
is LemonadeServer.exe --silent on Windows (ctx via LEMONADE_CTX_SIZE
env) and the lemond systemd unit on Linux. Add the stdlib-only shared
primitive (resolve_lemonade / get_installed_version /
build_start_command) that the installer and runtime client will adopt
instead of hard-coding lemonade-server.

Precedence: LEMONADE_SERVER_PATH env override (verbatim, no PATH
search) -> modern by canonical path (wins over a stale legacy binary on
PATH) -> legacy which(lemonade-server|lemonade-server-dev). Legacy argv
stays byte-identical (serve --ctx-size, + --no-tray on Windows).

All 12 contract tests in tests/unit/test_lemonade_launcher.py pass;
includes black formatting fixes to the contract test files.

check_installation() previously probed only shutil.which("lemonade-server"),
so a modern Lemonade install (10.7+, no lemonade-server CLI) reported
installed=False and gaia init tried to reinstall over a working setup.
Delegate detection to the shared resolve_lemonade()/get_installed_version()
primitive: modern installs are found at their canonical path, legacy
installs keep working unchanged, and a found install whose version probe
fails still reports installed=True with a diagnostic error (mirroring the
old failed-to-get-version branch). LemonadeInfo shape and find_product_code
are untouched — all five callers are unaffected.

…316)

Interactive `gaia init` previously never auto-started the server — an
indentation bug made the "Please start Lemonade Server" prompt block run
unconditionally, blocking on input() even in flows that could have
started the server themselves. Restructure _ensure_server_running():
auto-start is attempted first in BOTH CI (yes=True) and interactive
modes, success returns before any prompt, and the manual prompt is the
only remaining fall-through (interactive auto-start failure). CI mode
returns False on a failed auto-start without ever touching input().

Auto-start now routes through resolve_lemonade()/build_start_command()
in a new _auto_start_server() helper — the raw
[path, "serve", "--no-tray", --ctx-size] literal is gone, so modern
tooling (LemonadeServer.exe --silent + LEMONADE_CTX_SIZE env, merged
into the parent environment) starts correctly, including under CI's
LEMONADE_SERVER_PATH override which resolve_lemonade() now honors in
one place instead of a parallel os.environ.get. The interactive
fallback prompt renders the exact start command for the resolved
tooling; _find_lemonade_server() delegates to the shared primitive.

)

launch_server() hardcoded ["lemonade-server", "serve"], which no longer
exists in modern Lemonade (10.7+) — auto-start was broken for every
modern install. Route argv/env through
resolve_lemonade()/build_start_command(): modern gets
LemonadeServer.exe --silent with LEMONADE_CTX_SIZE merged into the
parent environment, legacy keeps its exact argv. A missing install now
raises an actionable LemonadeClientError instead of a bare
FileNotFoundError from Popen.

Also: skip kill_process_on_port() when health_check() already reports
OK at entry (never restart a healthy tray/systemd-managed server the
user didn't ask to restart); convert the "terminal" branch from a
shell=True f-string to argv-only Popen with CREATE_NEW_CONSOLE so a
resolved path never passes through a shell string; log_level appends
--log-level only for legacy tooling (modern launcher has no such flag —
logged at debug and ignored); _check_lemonade_installed() and
get_lemonade_version() use the primitive; user-facing "restart with"
hints render the resolved tooling's real start command instead of the
removed lemonade-server CLI (test assertion widened to accept the
modern LEMONADE_CTX_SIZE form).

…nned

TestLaunchServerCtxSize asserted the removed hardcoded lemonade-server
argv and hit the real network (unmocked health_check), so results
flipped depending on whether a local server happened to be running and
which tooling the host had. Pin resolve_lemonade to legacy (the argv
path under test — modern env-var ctx is covered by the #316 contract
tests) and stub health_check to fail so the already-healthy launch
guard never short-circuits the assertion.