fix: cost the device prefix exactly rather than approximately

The budget subtracted the prefix length plus two, on the assumption of a
leading and a trailing slash. That is right for /Music and wrong for an empty
prefix, where there is only one slash -- losing a character at the card root,
which is exactly where the longest paths sit.

Computed from the prefix as it will actually appear instead: /Music/ costs
seven characters and gives a mirror-relative budget of 253, the root costs one
and gives 259.

Worth being exact about because the reverse error is worse. A checker
comparing mirror-relative paths against the flat 260 passes everything between
253 and 260, and those are precisely the paths closest to the edge.

tools/check_fat32.py

@@ -28,6 +28,18 @@ PATH_LIMIT = 260
 DEVICE_PREFIX = "/Music"
 
 
+def device_prefix_length(prefix):
+    """Return the on-device prefix as it will actually appear, with slashes.
+
+    "/Music" costs seven characters -- the leading slash, the name, and the
+    separator before the mirror's own path -- while an empty prefix costs one.
+    Approximating that loses a character at the root, which is precisely where
+    the longest paths are.
+    """
+    cleaned = prefix.strip("/")
+    return f"/{cleaned}/" if cleaned else "/"
+
+
 def problems_with(relative, budget=PATH_LIMIT):
     """Return every reason this relative path is unfit for FAT32."""
     found = []
@@ -68,7 +80,7 @@ def main(argv=None):
         f" of the budget (default {DEVICE_PREFIX})",
     )
     args = parser.parse_args(argv)
-    budget = max(0, args.max_path - len(args.device_prefix.strip("/")) - 2)
+    budget = max(0, args.max_path - len(device_prefix_length(args.device_prefix)))
 
     root = Path(args.root)
     if not root.is_dir():