Add user profile management: display name + avatar upload (Gitea issue #12)

Users can set a display name (shown instead of username in the message
list, room member list, TopBar, and admin Users tab) and upload a real
avatar, replacing the generated color-initial avatars everywhere a user
appears. Avatars are square-cropped and downscaled to 512px, reusing
app/storage.py's upload primitives from image uploads with a new square
option.

Two deliberate divergences from message-image handling, documented in
backend/README.md: the previous avatar file is deleted on replace/remove
(safe since it's strictly one file per user), and avatar serving is not
room-gated and uses a short cache (identity-addressed and mutable, unlike
a message image's permanent content-addressed URL).

Frontend: new ProfileModal reachable from the TopBar account menu;
AuthContext gains updateUser() so a profile change reflects instantly
everywhere without a refetch.

backend/app/storage.py

@@ -48,12 +48,21 @@ async def read_capped(file, cap: int = MAX_IMAGE_BYTES) -> bytes:
     return b"".join(chunks)
 
 
-def process_image(data: bytes, content_type: str) -> tuple[bytes, str]:
+def process_image(
+    data: bytes,
+    content_type: str,
+    *,
+    square: bool = False,
+    max_dimension: int | None = None,
+) -> tuple[bytes, str]:
     """Confirms `data` is a genuinely decodable image (not just a spoofed
     Content-Type header) and downscales it so its longer side is
-    <=2000px -- except GIF, left untouched so animation isn't collapsed to
-    a single frame. Returns (final_bytes, storage_extension)."""
+    <=max_dimension (default 2000px) -- except GIF, left untouched so
+    animation isn't collapsed to a single frame. When `square` is set
+    (avatars), center-crops to the shorter side first. Returns
+    (final_bytes, storage_extension)."""
     ext, pillow_format = ALLOWED_IMAGE_CONTENT_TYPES[content_type]
+    dimension_cap = max_dimension or _MAX_DIMENSION
 
     try:
         with Image.open(io.BytesIO(data)) as probe:
@@ -69,7 +78,12 @@ def process_image(data: bytes, content_type: str) -> tuple[bytes, str]:
     image.load()
     if pillow_format == "JPEG" and image.mode in ("RGBA", "P"):
         image = image.convert("RGB")
-    image.thumbnail((_MAX_DIMENSION, _MAX_DIMENSION))
+    if square:
+        side = min(image.width, image.height)
+        left = (image.width - side) // 2
+        top = (image.height - side) // 2
+        image = image.crop((left, top, left + side, top + side))
+    image.thumbnail((dimension_cap, dimension_cap))
     out = io.BytesIO()
     image.save(out, format=pillow_format)
     return out.getvalue(), ext
@@ -80,3 +94,9 @@ def save_image(data: bytes, ext: str) -> str:
     storage_filename = f"{uuid.uuid4()}{ext}"
     (UPLOADS_DIR / storage_filename).write_bytes(data)
     return storage_filename
+
+
+def delete_image(storage_filename: str) -> None:
+    """Best-effort delete -- a missing file (already gone, or never
+    written) is not an error."""
+    (UPLOADS_DIR / storage_filename).unlink(missing_ok=True)