feat: add user display profiles and fix web context menu UX

backend:

- add required user name and optional bio fields

- extend auth/register and user schemas/services with name/bio

- add alembic migration 0006 with safe backfill name=username

- compute per-user chat display_title for private chats

- keep Saved Messages delete-for-all protections

web:

- registration now includes name

- add profile edit modal (name/username/bio/avatar url)

- show private chat names via display_title

- fix context menus to open near cursor with viewport clamping

- stabilize +/close floating button to remove visual jump

web/src/components/NewChatPanel.tsx

@@ -13,6 +13,7 @@ export function NewChatPanel() {
   const [title, setTitle] = useState("");
   const [handle, setHandle] = useState("");
   const [description, setDescription] = useState("");
+  const [isPublic, setIsPublic] = useState(false);
   const [results, setResults] = useState<UserSearchItem[]>([]);
   const [discoverResults, setDiscoverResults] = useState<DiscoverChat[]>([]);
   const [loading, setLoading] = useState(false);
@@ -87,8 +88,14 @@ export function NewChatPanel() {
     setError(null);
     try {
       let chat;
-      if (handle.trim()) {
-        chat = await createPublicChat(mode, title.trim(), handle.trim().replace("@", "").toLowerCase(), description.trim() || undefined);
+      if (isPublic) {
+        const normalizedHandle = handle.trim().replace("@", "").toLowerCase();
+        if (!normalizedHandle) {
+          setError("Public chat requires @handle");
+          setLoading(false);
+          return;
+        }
+        chat = await createPublicChat(mode, title.trim(), normalizedHandle, description.trim() || undefined);
       } else {
         chat = await createChat(mode as ChatType, title.trim(), []);
       }
@@ -97,6 +104,7 @@ export function NewChatPanel() {
       setTitle("");
       setHandle("");
       setDescription("");
+      setIsPublic(false);
     } catch {
       setError("Failed to create chat");
     } finally {
@@ -124,6 +132,7 @@ export function NewChatPanel() {
     setQuery("");
     setResults([]);
     setDiscoverResults([]);
+    setIsPublic(false);
   }
 
   return (
@@ -148,8 +157,8 @@ export function NewChatPanel() {
             </button>
           </div>
         ) : null}
-        <button className="h-12 w-12 rounded-full bg-sky-500 text-xl font-semibold text-slate-950 shadow-lg hover:bg-sky-400" onClick={() => setMenuOpen((v) => !v)}>
-          {menuOpen ? "×" : "+"}
+        <button className="flex h-12 w-12 items-center justify-center rounded-full bg-sky-500 text-slate-950 shadow-lg hover:bg-sky-400" onClick={() => setMenuOpen((v) => !v)}>
+          <span className="block w-5 text-center text-2xl leading-none">{menuOpen ? "✕" : "+"}</span>
         </button>
       </div>
 
@@ -169,7 +178,8 @@ export function NewChatPanel() {
                 <div className="tg-scrollbar max-h-44 overflow-auto">
                   {results.map((user) => (
                     <button className="mb-1 block w-full rounded-lg bg-slate-800 px-3 py-2 text-left text-sm hover:bg-slate-700" key={user.id} onClick={() => void createPrivate(user.id)}>
-                      @{user.username}
+                      <p className="truncate font-semibold">{user.name}</p>
+                      <p className="truncate text-xs text-slate-400">@{user.username}</p>
                     </button>
                   ))}
                   {normalizedQuery && results.length === 0 ? <p className="text-xs text-slate-400">No users</p> : null}
@@ -180,6 +190,7 @@ export function NewChatPanel() {
             {dialog === "discover" ? (
               <div className="space-y-2">
                 <input className="w-full rounded-xl border border-slate-700/80 bg-slate-800/80 px-3 py-2 text-sm outline-none placeholder:text-slate-400 focus:border-sky-500" placeholder="Search groups/channels by title or @handle" value={query} onChange={(e) => void handleDiscover(e.target.value)} />
+                <p className="text-xs text-slate-400">Search works only for public groups/channels.</p>
                 <div className="tg-scrollbar max-h-52 overflow-auto">
                   {discoverResults.map((chat) => (
                     <div className="mb-1 flex items-center justify-between rounded-lg bg-slate-800 px-3 py-2" key={chat.id}>
@@ -204,7 +215,13 @@ export function NewChatPanel() {
             {dialog === "group" || dialog === "channel" ? (
               <form className="space-y-2" onSubmit={(e) => void createByType(e, dialog)}>
                 <input className="w-full rounded-xl border border-slate-700/80 bg-slate-800/80 px-3 py-2 text-sm outline-none placeholder:text-slate-400 focus:border-sky-500" placeholder={dialog === "group" ? "Group title" : "Channel title"} value={title} onChange={(e) => setTitle(e.target.value)} />
-                <input className="w-full rounded-xl border border-slate-700/80 bg-slate-800/80 px-3 py-2 text-sm outline-none placeholder:text-slate-400 focus:border-sky-500" placeholder="@handle (optional, enables public join/search)" value={handle} onChange={(e) => setHandle(e.target.value)} />
+                <label className="flex items-center gap-2 rounded-xl border border-slate-700/80 bg-slate-800/60 px-3 py-2 text-sm">
+                  <input checked={isPublic} onChange={(e) => setIsPublic(e.target.checked)} type="checkbox" />
+                  Public {dialog} (discover + join by others)
+                </label>
+                {isPublic ? (
+                  <input className="w-full rounded-xl border border-slate-700/80 bg-slate-800/80 px-3 py-2 text-sm outline-none placeholder:text-slate-400 focus:border-sky-500" placeholder="@handle (required for public)" value={handle} onChange={(e) => setHandle(e.target.value)} />
+                ) : null}
                 <input className="w-full rounded-xl border border-slate-700/80 bg-slate-800/80 px-3 py-2 text-sm outline-none placeholder:text-slate-400 focus:border-sky-500" placeholder="Description (optional)" value={description} onChange={(e) => setDescription(e.target.value)} />
                 <button className="w-full rounded-lg bg-sky-500 px-3 py-2 text-sm font-semibold text-slate-950 hover:bg-sky-400 disabled:opacity-60" disabled={loading} type="submit">
                   Create {dialog}