feat(library/providers): let a provider say how to recognize its games

A plugin's titles launch through the provider's own client, which hands off and
exits — so the host had nothing left to watch, and both lifetime behaviors went
quiet for exactly the entries a provider contributes. A `ProviderEntry` (and a
manual custom entry) may now carry an optional `detect` hint: install dir, exe,
or process name.

It is deliberately a subset of what the host tracks internally. A Steam appid or
a launcher's environment marker are things the host discovers for itself and
would be meaningless — or dangerous — to take on someone's word; where a title
is installed is something only the provider knows. The host's own findings win
where both exist, so a stale export can never redirect the matcher, and a blank
field is treated as absent rather than as "match everything" — an empty install
dir would otherwise prefix-match every process on the box, and this feature can
end processes.

`process_name` is the weakest of the three and the only one typed by hand, so it
is matched case-insensitively against the image's file name and nothing else:
`retroarch` finds RetroArch, not a helper whose name merely starts the same way,
and not a script that happens to live in a `retroarch/` directory. The
never-adopt-a-pre-existing-process rule still bounds it.

Also: the tray summary gains the running-game row (with the closing-in countdown
for a game whose client is gone — visible at the machine without opening the
console), the SDK mirrors the `game.*` events, and its generated client catches
up with the endpoints Phase 1 added.

Gates on .21: check + clippy --all-targets clean, 299 tests, fmt CI-parity,
openapi regenerated (GameEntry still carries no `detect` outbound); SDK tsc +
54 tests green.

crates/punktfunk-host/src/mgmt/host.rs

@@ -207,6 +207,13 @@ pub(crate) struct LocalSummary {
     /// the tray/console surface them so the clash is visible before pairing silently fails.
     #[serde(default, skip_serializing_if = "Vec::is_empty")]
     conflicts: Vec<String>,
+    /// Launched games the host is tracking, as compact labels (`Hades`, `Hades (closing in 4:12)`).
+    ///
+    /// The countdown form is the one that matters: it means the game's client is gone and the host
+    /// will end the game when the window closes — something a user at the machine should be able to
+    /// see (and stop) without opening the console. Empty when nothing was launched.
+    #[serde(default, skip_serializing_if = "Vec::is_empty")]
+    games: Vec<String>,
 }
 
 /// Liveness probe
@@ -489,5 +496,12 @@ pub(crate) async fn get_local_summary(State(st): State<Arc<MgmtState>>) -> Json<
         // Cached at `serve` startup (empty when nothing was detected / never scanned) — no per-poll
         // process enumeration.
         conflicts: crate::detect::summary_labels(crate::detect::snapshot()),
+        games: crate::session_status::games()
+            .into_iter()
+            .map(|g| match g.grace_remaining_s {
+                Some(left) => format!("{} (closing in {}:{:02})", g.title, left / 60, left % 60),
+                None => g.title,
+            })
+            .collect(),
     })
 }