fix(store): use string prefix + URLSearchParams for connection URL parsing

The URL constructor parses non-standard protocols (multica://)
differently across engines — Chromium may return empty hostname
while Node.js returns "connect". Replace new URL() with simple
startsWith check and URLSearchParams to ensure consistent behavior
in both web and Electron environments.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

packages/store/src/connection.ts

@@ -22,10 +22,50 @@ function isConnectionInfo(obj: unknown): obj is ConnectionInfo {
   )
 }
 
+// Parse multica://connect?gateway=...&hub=...&agent=...&token=...&exp=... URL format
+// Uses string prefix + URLSearchParams to avoid cross-engine URL hostname differences
+function parseConnectionUrl(input: string): ConnectionInfo | null {
+  const prefix = "multica://connect?"
+  if (!input.startsWith(prefix)) return null
+  try {
+    const params = new URLSearchParams(input.slice(prefix.length))
+    const gateway = params.get("gateway")
+    const hubId = params.get("hub")
+    const agentId = params.get("agent")
+    const token = params.get("token")
+    const exp = params.get("exp")
+    if (!gateway || !hubId || !agentId || !token || !exp) return null
+    return {
+      type: "multica-connect",
+      gateway,
+      hubId,
+      agentId,
+      token,
+      expires: Number(exp),
+    }
+  } catch {
+    return null
+  }
+}
+
+function isExpired(expires: number): boolean {
+  // Desktop generates expires as millisecond timestamp (Date.now() + seconds * 1000)
+  return Date.now() > expires
+}
+
 export function parseConnectionCode(input: string): ConnectionInfo {
   const trimmed = input.trim()
 
-  // Try JSON first
+  // Try multica:// URL format first (desktop "Copy Link" output)
+  const fromUrl = parseConnectionUrl(trimmed)
+  if (fromUrl) {
+    if (isExpired(fromUrl.expires)) {
+      throw new Error("Connection code has expired")
+    }
+    return fromUrl
+  }
+
+  // Try JSON (QR code scan output)
   let parsed: unknown
   try {
     parsed = JSON.parse(trimmed)
@@ -42,7 +82,7 @@ export function parseConnectionCode(input: string): ConnectionInfo {
     throw new Error("Invalid connection code format")
   }
 
-  if (Date.now() > parsed.expires * 1000) {
+  if (isExpired(parsed.expires)) {
     throw new Error("Connection code has expired")
   }
 
@@ -60,7 +100,7 @@ export function loadConnection(): ConnectionInfo | null {
   try {
     const info = JSON.parse(raw)
     if (!isConnectionInfo(info)) return null
-    if (Date.now() > info.expires * 1000) {
+    if (isExpired(info.expires)) {
       localStorage.removeItem(STORAGE_KEY)
       return null
     }