Home-screen tile via sceAppInstUtilAppInstallTitleDir

Write param.json + icon0.png into /user/app/<TITLE_ID>/sce_sys/, then
call sceAppInstUtilAppInstallTitleDir to register the directory as an
app. No package, no code signing — the installer reads the metadata
files directly.

The tile uses TITLE_ID PTDL00001 and deeplinkUri
http://127.0.0.1:12880/, so tapping it opens PatchDL's own UI in the
on-console browser. Only useful while the ELF is running.

Asset pipeline: param.json + icon0.png live under assets/ and get
.incbin'd straight into .rodata. Makefile lists them as TILE_ASSETS so
a touch on either forces a relink.

Stat-guard: file_matches() diffs each asset against the on-disk copy
first; when nothing changed the install API isn't called at all. Keeps
repeated payload starts from re-registering the app. Repeated
/api/install_tile calls return "already installed and up to date".

Backend lazy-load: AppInstUtil isn't mapped until something pokes it,
so the helper polls patchdl_install_backend_check() for up to ~15 s
before resolving sceAppInstUtilAppInstallTitleDir.

Wiring: /api/install_tile POST triggers the install on demand;
patchdl_websrv_start() runs it at startup when home_shortcut is on;
and flipping the toggle from off to on in /api/config also fires it.
All three paths share the stat-guarded helper so they're safe to
repeat.

Makefile

@@ -23,7 +23,12 @@ SRCS := src/main.c \
         src/patchdl_resolve.c \
         src/patchdl_verxml.c \
         src/patchdl_install.c \
-        src/patchdl_notify.c
+        src/patchdl_notify.c \
+        src/patchdl_tile.c
+
+# patchdl_tile.c uses .incbin to embed param.json + icon0.png; touching the
+# assets must trigger a rebuild.
+TILE_ASSETS := assets/param.json assets/icon0.png
 
 WEB_ASSETS := web/index.html web/styles.css web/app.js
 GEN_SRCS := $(patsubst web/%,gen/web/%.c,$(WEB_ASSETS))
@@ -56,8 +61,8 @@ gen/web/%.c: web/% scripts/gen_asset_module.py | gen/web
 $(SQLITE_OBJ): $(SQLITE_DIR)/sqlite3.c
 	$(CC) $(SQLITE_CFLAGS) -c -o $@ $<
 
-$(BIN): $(SRCS) $(GEN_SRCS) $(SQLITE_OBJ)
-	$(CC) $(CFLAGS) -o $@ $^ $(LDADD)
+$(BIN): $(SRCS) $(GEN_SRCS) $(SQLITE_OBJ) $(TILE_ASSETS)
+	$(CC) $(CFLAGS) -o $@ $(SRCS) $(GEN_SRCS) $(SQLITE_OBJ) $(LDADD)
 
 test: $(BIN)
 	$(PS5_DEPLOY) -h $(PS5_HOST) -p $(PS5_PORT) $^